Resultado de la búsqueda
43 búsqueda de la palabra clave 'Field'
Refinar búsqueda Generar rss de la búsqueda
Link de la búsqueda
Título : Field Arithmetic Tipo de documento: documento electrónico Autores: Fried, Michael D ; SpringerLink (Online service) ; Jarden, Moshe Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Colección: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, ISSN 0071-1136 num. 11 Número de páginas: XXIV, 792 p Il.: online resource ISBN/ISSN/DL: 978-3-540-77270-5 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Field theory (Physics) Geometry Mathematical logic Mathematics, general Theory and Polynomials Logic Foundations Clasificación: 51 Matemáticas Resumen: Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005 Nota de contenido: Infinite Galois Theory and Profinite Groups -- Valuations and Linear Disjointness -- Algebraic Function Fields of One Variable -- The Riemann Hypothesis for Function Fields -- Plane Curves -- The Chebotarev Density Theorem -- Ultraproducts -- Decision Procedures -- Algebraically Closed Fields -- Elements of Algebraic Geometry -- Pseudo Algebraically Closed Fields -- Hilbertian Fields -- The Classical Hilbertian Fields -- Nonstandard Structures -- Nonstandard Approach to Hilbert’s Irreducibility Theorem -- Galois Groups over Hilbertian Fields -- Free Profinite Groups -- The Haar Measure -- Effective Field Theory and Algebraic Geometry -- The Elementary Theory of e-Free PAC Fields -- Problems of Arithmetical Geometry -- Projective Groups and Frattini Covers -- PAC Fields and Projective Absolute Galois Groups -- Frobenius Fields -- Free Profinite Groups of Infinite Rank -- Random Elements in Profinite Groups -- Omega-Free PAC Fields -- Undecidability -- Algebraically Closed Fields with Distinguished Automorphisms -- Galois Stratification -- Galois Stratification over Finite Fields -- Problems of Field Arithmetic En línea: http://dx.doi.org/10.1007/978-3-540-77270-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34366 Field Arithmetic [documento electrónico] / Fried, Michael D ; SpringerLink (Online service) ; Jarden, Moshe . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - XXIV, 792 p : online resource. - (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, ISSN 0071-1136; 11) .
ISBN : 978-3-540-77270-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Field theory (Physics) Geometry Mathematical logic Mathematics, general Theory and Polynomials Logic Foundations Clasificación: 51 Matemáticas Resumen: Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? The third edition improves the second edition in two ways: First it removes many typos and mathematical inaccuracies that occur in the second edition (in particular in the references). Secondly, the third edition reports on five open problems (out of thirtyfour open problems of the second edition) that have been partially or fully solved since that edition appeared in 2005 Nota de contenido: Infinite Galois Theory and Profinite Groups -- Valuations and Linear Disjointness -- Algebraic Function Fields of One Variable -- The Riemann Hypothesis for Function Fields -- Plane Curves -- The Chebotarev Density Theorem -- Ultraproducts -- Decision Procedures -- Algebraically Closed Fields -- Elements of Algebraic Geometry -- Pseudo Algebraically Closed Fields -- Hilbertian Fields -- The Classical Hilbertian Fields -- Nonstandard Structures -- Nonstandard Approach to Hilbert’s Irreducibility Theorem -- Galois Groups over Hilbertian Fields -- Free Profinite Groups -- The Haar Measure -- Effective Field Theory and Algebraic Geometry -- The Elementary Theory of e-Free PAC Fields -- Problems of Arithmetical Geometry -- Projective Groups and Frattini Covers -- PAC Fields and Projective Absolute Galois Groups -- Frobenius Fields -- Free Profinite Groups of Infinite Rank -- Random Elements in Profinite Groups -- Omega-Free PAC Fields -- Undecidability -- Algebraically Closed Fields with Distinguished Automorphisms -- Galois Stratification -- Galois Stratification over Finite Fields -- Problems of Field Arithmetic En línea: http://dx.doi.org/10.1007/978-3-540-77270-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34366 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : Field Arithmetic Tipo de documento: documento electrónico Autores: Fried, Michael D ; SpringerLink (Online service) ; Jarden, Moshe Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: A Series of Modern Surveys in Mathematics num. 11 Número de páginas: XXIII, 780 p Il.: online resource ISBN/ISSN/DL: 978-3-540-26949-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Field theory (Physics) Geometry Mathematical logic Number Theory and Polynomials Logic Foundations Clasificación: 51 Matemáticas Resumen: Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? Nota de contenido: Infinite Galois Theory and Profinite Groups -- Valuations and Linear Disjointness -- Algebraic Function Fields of One Variable -- The Riemann Hypothesis for Function Fields -- Plane Curves -- The Chebotarev Density Theorem -- Ultraproducts -- Decision Procedures -- Algebraically Closed Fields -- Elements of Algebraic Geometry -- Pseudo Algebraically Closed Fields -- Hilbertian Fields -- The Classical Hilbertian Fields -- Nonstandard Structures -- Nonstandard Approach to Hilbert’s Irreducibility Theorem -- Galois Groups over Hilbertian Fields -- Free Profinite Groups -- The Haar Measure -- Effective Field Theory and Algebraic Geometry -- The Elementary Theory of e-Free PAC Fields -- Problems of Arithmetical Geometry -- Projective Groups and Frattini Covers -- PAC Fields and Projective Absolute Galois Groups -- Frobenius Fields -- Free Profinite Groups of Infinite Rank -- Random Elements in Profinite Groups -- Omega-free PAC Fields -- Undecidability -- Algebraically Closed Fields with Distinguished Automorphisms -- Galois Stratification -- Galois Stratification over Finite Fields -- Problems of Field Arithmetic En línea: http://dx.doi.org/10.1007/b138352 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35258 Field Arithmetic [documento electrónico] / Fried, Michael D ; SpringerLink (Online service) ; Jarden, Moshe . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XXIII, 780 p : online resource. - (A Series of Modern Surveys in Mathematics; 11) .
ISBN : 978-3-540-26949-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Field theory (Physics) Geometry Mathematical logic Number Theory and Polynomials Logic Foundations Clasificación: 51 Matemáticas Resumen: Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements. Progress from the first edition starts by characterizing the finite-field like P(seudo)A(lgebraically)C(losed) fields. We once believed PAC fields were rare. Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)? Nota de contenido: Infinite Galois Theory and Profinite Groups -- Valuations and Linear Disjointness -- Algebraic Function Fields of One Variable -- The Riemann Hypothesis for Function Fields -- Plane Curves -- The Chebotarev Density Theorem -- Ultraproducts -- Decision Procedures -- Algebraically Closed Fields -- Elements of Algebraic Geometry -- Pseudo Algebraically Closed Fields -- Hilbertian Fields -- The Classical Hilbertian Fields -- Nonstandard Structures -- Nonstandard Approach to Hilbert’s Irreducibility Theorem -- Galois Groups over Hilbertian Fields -- Free Profinite Groups -- The Haar Measure -- Effective Field Theory and Algebraic Geometry -- The Elementary Theory of e-Free PAC Fields -- Problems of Arithmetical Geometry -- Projective Groups and Frattini Covers -- PAC Fields and Projective Absolute Galois Groups -- Frobenius Fields -- Free Profinite Groups of Infinite Rank -- Random Elements in Profinite Groups -- Omega-free PAC Fields -- Undecidability -- Algebraically Closed Fields with Distinguished Automorphisms -- Galois Stratification -- Galois Stratification over Finite Fields -- Problems of Field Arithmetic En línea: http://dx.doi.org/10.1007/b138352 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35258 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : Field Theory Tipo de documento: documento electrónico Autores: Roman, Steven ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 158 Número de páginas: XII, 335 p. 18 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-27678-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Field theory (Physics) Number Theory and Polynomials Clasificación: 51 Matemáticas Resumen: This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity. For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities. From the reviews of the first edition: The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study. - T. Albu, Mathematical Reviews ...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study. - J.N.Mordeson, Zentralblatt Nota de contenido: Preliminaries -- Preliminaries -- Field Extensions -- Polynomials -- Field Extensions -- Embeddings and Separability -- Algebraic Independence -- Galois Theory -- Galois Theory I: An Historical Perspective -- Galois Theory II: The Theory -- Galois Theory III: The Galois Group of a Polynomial -- A Field Extension as a Vector Space -- Finite Fields I: Basic Properties -- Finite Fields II: Additional Properties -- The Roots of Unity -- Cyclic Extensions -- Solvable Extensions -- The Theory of Binomials -- Binomials -- Families of Binomials En línea: http://dx.doi.org/10.1007/0-387-27678-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34742 Field Theory [documento electrónico] / Roman, Steven ; SpringerLink (Online service) . - New York, NY : Springer New York, 2006 . - XII, 335 p. 18 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 158) .
ISBN : 978-0-387-27678-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Field theory (Physics) Number Theory and Polynomials Clasificación: 51 Matemáticas Resumen: This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity. For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities. From the reviews of the first edition: The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study. - T. Albu, Mathematical Reviews ...[the author] does an excellent job of stressing the key ideas. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study. - J.N.Mordeson, Zentralblatt Nota de contenido: Preliminaries -- Preliminaries -- Field Extensions -- Polynomials -- Field Extensions -- Embeddings and Separability -- Algebraic Independence -- Galois Theory -- Galois Theory I: An Historical Perspective -- Galois Theory II: The Theory -- Galois Theory III: The Galois Group of a Polynomial -- A Field Extension as a Vector Space -- Finite Fields I: Basic Properties -- Finite Fields II: Additional Properties -- The Roots of Unity -- Cyclic Extensions -- Solvable Extensions -- The Theory of Binomials -- Binomials -- Families of Binomials En línea: http://dx.doi.org/10.1007/0-387-27678-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34742 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : A Field Guide to Algebra Tipo de documento: documento electrónico Autores: Chambert-Loir, Antoine ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2005 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: X, 198 p Il.: online resource ISBN/ISSN/DL: 978-0-387-26955-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Commutative algebra rings Field theory (Physics) Number Theory and Polynomials Rings Algebras Clasificación: 51 Matemáticas Resumen: This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths. In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians. Antoine Chambert-Loir taught this book when he was Professor at École polytechnique, Palaiseau, France. He is now Professor at Université de Rennes 1 Nota de contenido: Field extensions -- Roots -- Galois theory -- A bit of group theory -- Applications -- Algebraic theory of differential equations En línea: http://dx.doi.org/10.1007/b138364 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35104 A Field Guide to Algebra [documento electrónico] / Chambert-Loir, Antoine ; SpringerLink (Online service) . - New York, NY : Springer New York, 2005 . - X, 198 p : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-26955-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Commutative algebra rings Field theory (Physics) Number Theory and Polynomials Rings Algebras Clasificación: 51 Matemáticas Resumen: This unique textbook focuses on the structure of fields and is intended for a second course in abstract algebra. Besides providing proofs of the transcendance of pi and e, the book includes material on differential Galois groups and a proof of Hilbert's irreducibility theorem. The reader will hear about equations, both polynomial and differential, and about the algebraic structure of their solutions. In explaining these concepts, the author also provides comments on their historical development and leads the reader along many interesting paths. In addition, there are theorems from analysis: as stated before, the transcendence of the numbers pi and e, the fact that the complex numbers form an algebraically closed field, and also Puiseux's theorem that shows how one can parametrize the roots of polynomial equations, the coefficients of which are allowed to vary. There are exercises at the end of each chapter, varying in degree from easy to difficult. To make the book more lively, the author has incorporated pictures from the history of mathematics, including scans of mathematical stamps and pictures of mathematicians. Antoine Chambert-Loir taught this book when he was Professor at École polytechnique, Palaiseau, France. He is now Professor at Université de Rennes 1 Nota de contenido: Field extensions -- Roots -- Galois theory -- A bit of group theory -- Applications -- Algebraic theory of differential equations En línea: http://dx.doi.org/10.1007/b138364 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35104 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : Algebra : Fields and Galois Theory Tipo de documento: documento electrónico Autores: Lorenz, Falko ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2006 Colección: Universitext, ISSN 0172-5939 Número de páginas: VIII, 296 p. 6 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-31608-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Commutative algebra rings Field theory (Physics) Number Theory and Polynomials Rings Algebras Clasificación: 51 Matemáticas Resumen: The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, diophantine dimensions of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the German version: This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews Nota de contenido: Constructibility with Ruler and Compass -- Algebraic Extensions -- Simple Extensions -- Fundamentals of Divisibility -- Prime Factorization in Polynomial Rings. Gauss’s Theorem -- Polynomial Splitting Fields -- Separable Extensions -- Galois Extensions -- Finite Fields, Cyclic Groups and Roots of Unity -- Group Actions -- Applications of Galois Theory to Cyclotomic Fields -- Further Steps into Galois Theory -- Norm and Trace -- Binomial Equations -- Solvability of Equations -- Integral Ring Extensions with Applications to Galois Theory -- The Transcendence of ? -- Fundamentals of Transcendental Field Extensions -- Hilbert’s Nullstellensatz En línea: http://dx.doi.org/10.1007/0-387-31608-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34789 Algebra : Fields and Galois Theory [documento electrónico] / Lorenz, Falko ; SpringerLink (Online service) . - New York, NY : Springer New York, 2006 . - VIII, 296 p. 6 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-0-387-31608-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Commutative algebra rings Field theory (Physics) Number Theory and Polynomials Rings Algebras Clasificación: 51 Matemáticas Resumen: The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, diophantine dimensions of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory. Both volumes contain numerous exercises and can be used as a textbook for advanced undergraduate students. From Reviews of the German version: This is a charming textbook, introducing the reader to the classical parts of algebra. The exposition is admirably clear and lucidly written with only minimal prerequisites from linear algebra. The new concepts are, at least in the first part of the book, defined in the framework of the development of carefully selected problems. - Stefan Porubsky, Mathematical Reviews Nota de contenido: Constructibility with Ruler and Compass -- Algebraic Extensions -- Simple Extensions -- Fundamentals of Divisibility -- Prime Factorization in Polynomial Rings. Gauss’s Theorem -- Polynomial Splitting Fields -- Separable Extensions -- Galois Extensions -- Finite Fields, Cyclic Groups and Roots of Unity -- Group Actions -- Applications of Galois Theory to Cyclotomic Fields -- Further Steps into Galois Theory -- Norm and Trace -- Binomial Equations -- Solvability of Equations -- Integral Ring Extensions with Applications to Galois Theory -- The Transcendence of ? -- Fundamentals of Transcendental Field Extensions -- Hilbert’s Nullstellensatz En línea: http://dx.doi.org/10.1007/0-387-31608-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34789 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar PermalinkPermalinkPermalinkFinitely Generated Abelian Groups and Similarity of Matrices over a Field / Norman, Christopher (2012)
Permalink
Permalink
