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Título : Algebraic Geometry and Commutative Algebra Tipo de documento: documento electrónico Autores: Siegfried Bosch ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 504 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-4829-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Geometry Rings and Algebras Clasificación: 51 Matemáticas Resumen: Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature Nota de contenido: Rings and Modules -- The Theory of Noetherian Rings -- Integral Extensions -- Extension of Coefficients and Descent -- Homological Methods: Ext and Tor -- Affine Schemes and Basic Constructions -- Techniques of Global Schemes -- Etale and Smooth Morphisms -- Projective Schemes and Proper Morphisms En línea: http://dx.doi.org/10.1007/978-1-4471-4829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32195 Algebraic Geometry and Commutative Algebra [documento electrónico] / Siegfried Bosch ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - X, 504 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-4829-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Geometry Rings and Algebras Clasificación: 51 Matemáticas Resumen: Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature Nota de contenido: Rings and Modules -- The Theory of Noetherian Rings -- Integral Extensions -- Extension of Coefficients and Descent -- Homological Methods: Ext and Tor -- Affine Schemes and Basic Constructions -- Techniques of Global Schemes -- Etale and Smooth Morphisms -- Projective Schemes and Proper Morphisms En línea: http://dx.doi.org/10.1007/978-1-4471-4829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32195 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Algebras, Rings and Modules / SpringerLink (Online service) ; Michiel Hazewinkel ; Nadiya Gubareni ; Kirichenko, V. V. (2007)
Título : Algebras, Rings and Modules Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Michiel Hazewinkel ; Nadiya Gubareni ; Kirichenko, V. V. Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2007 Colección: Mathematics and Its Applications num. 586 Número de páginas: XII, 400 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-5141-8 Idioma : Inglés (eng) Palabras clave: Mathematics Associative rings Rings (Algebra) Category theory (Mathematics) Homological algebra Commutative Matrix Algebra and Algebras Theory, Linear Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined. The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings. Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest Nota de contenido: Groups and group representations -- Quivers and their representations -- Representations of posets and of finite dimensional algebras -- Frobenius algebras and quasi-Frobenius rings -- Right serial rings -- Tiled orders over discrete valuation rings -- Gorenstein matrices En línea: http://dx.doi.org/10.1007/978-1-4020-5141-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34573 Algebras, Rings and Modules [documento electrónico] / SpringerLink (Online service) ; Michiel Hazewinkel ; Nadiya Gubareni ; Kirichenko, V. V. . - Dordrecht : Springer Netherlands, 2007 . - XII, 400 p : online resource. - (Mathematics and Its Applications; 586) .
ISBN : 978-1-4020-5141-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Associative rings Rings (Algebra) Category theory (Mathematics) Homological algebra Commutative Matrix Algebra and Algebras Theory, Linear Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: As a natural continuation of the first volume of Algebras, Rings and Modules, this book provides both the classical aspects of the theory of groups and their representations as well as a general introduction to the modern theory of representations including the representations of quivers and finite partially ordered sets and their applications to finite dimensional algebras. Detailed attention is given to special classes of algebras and rings including Frobenius, quasi-Frobenius, right serial rings and tiled orders using the technique of quivers. The most important recent developments in the theory of these rings are examined. The Cartan Determinant Conjecture and some properties of global dimensions of different classes of rings are also given. The last chapters of this volume provide the theory of semiprime Noetherian semiperfect and semidistributive rings. Of course, this book is mainly aimed at researchers in the theory of rings and algebras but graduate and postgraduate students, especially those using algebraic techniques, should also find this book of interest Nota de contenido: Groups and group representations -- Quivers and their representations -- Representations of posets and of finite dimensional algebras -- Frobenius algebras and quasi-Frobenius rings -- Right serial rings -- Tiled orders over discrete valuation rings -- Gorenstein matrices En línea: http://dx.doi.org/10.1007/978-1-4020-5141-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34573 Ejemplares
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Título : Algebras, Rings and Modules : Volume 1 Tipo de documento: documento electrónico Autores: Michiel Hazewinkel ; SpringerLink (Online service) ; Nadiya Gubareni ; Kirichenko, V. V. Editorial: Dordrecht : Springer Netherlands Fecha de publicación: 2005 Colección: Mathematics and Its Applications num. 575 Número de páginas: XII, 380 p Il.: online resource ISBN/ISSN/DL: 978-1-4020-2691-1 Idioma : Inglés (eng) Palabras clave: Mathematics Associative rings Rings (Algebra) Commutative algebra and Algebras Clasificación: 51 Matemáticas Nota de contenido: Preliminaries -- Decompositions of rings -- Artinian and Noetherian rings -- Categories and functors -- Projectives, injectives and flats -- Homological dimensions -- Integral domains -- Dedekind domains -- Goldie rings -- Semiperfect rings -- Quivers of rings -- Serial rings and modules -- Serial rings and their properties -- Semiperfect semidistributive rings En línea: http://dx.doi.org/10.1007/1-4020-2691-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35204 Algebras, Rings and Modules : Volume 1 [documento electrónico] / Michiel Hazewinkel ; SpringerLink (Online service) ; Nadiya Gubareni ; Kirichenko, V. V. . - Dordrecht : Springer Netherlands, 2005 . - XII, 380 p : online resource. - (Mathematics and Its Applications; 575) .
ISBN : 978-1-4020-2691-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Associative rings Rings (Algebra) Commutative algebra and Algebras Clasificación: 51 Matemáticas Nota de contenido: Preliminaries -- Decompositions of rings -- Artinian and Noetherian rings -- Categories and functors -- Projectives, injectives and flats -- Homological dimensions -- Integral domains -- Dedekind domains -- Goldie rings -- Semiperfect rings -- Quivers of rings -- Serial rings and modules -- Serial rings and their properties -- Semiperfect semidistributive rings En línea: http://dx.doi.org/10.1007/1-4020-2691-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35204 Ejemplares
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Título : Exercises in Modules and Rings Tipo de documento: documento electrónico Autores: Tsit Yuen Lam ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Problem Books in Mathematics, ISSN 0941-3502 Número de páginas: XVIII, 414 p Il.: online resource ISBN/ISSN/DL: 978-0-387-48899-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) and Algebras Clasificación: 51 Matemáticas Resumen: For the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie’s theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita’s classical theory of category dualities and equivalences. Each of the nineteen sections begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements, generalizations, and latent connections to other problems. This volume is designed as a problem book for the author’s Lectures on Modules and Rings (Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as a source for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of the author’s lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classical Ring Theory (Springer, 2003) offer to the mathematics community the fullest and most comprehensive reference to date for problem solving in the theory of modules and rings Nota de contenido: Free Modules, Projective, and Injective Modules -- Flat Modules and Homological Dimensions -- More Theory of Modules -- Rings of Quotients -- More Rings of Quotients -- Frobenius and Quasi-Frobenius Rings -- Matrix Rings, Categories of Modules and Morita Theory En línea: http://dx.doi.org/10.1007/978-0-387-48899-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34480 Exercises in Modules and Rings [documento electrónico] / Tsit Yuen Lam ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XVIII, 414 p : online resource. - (Problem Books in Mathematics, ISSN 0941-3502) .
ISBN : 978-0-387-48899-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Associative rings Rings (Algebra) and Algebras Clasificación: 51 Matemáticas Resumen: For the Backcover This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie’s theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita’s classical theory of category dualities and equivalences. Each of the nineteen sections begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements, generalizations, and latent connections to other problems. This volume is designed as a problem book for the author’s Lectures on Modules and Rings (Springer GTM, Vol. 189), from which the majority of the exercises were taken. Some forty new exercises have been added to further broaden the coverage. As a result, this book is ideal both as a companion volume to Lectures, and as a source for independent study. For students and researchers alike, this book will also serve as a handy reference for a copious amount of information in algebra and ring theory otherwise unavailable from textbooks. An outgrowth of the author’s lecture courses and seminars over the years at the University of California at Berkeley, this book and its predecessor Exercises in Classical Ring Theory (Springer, 2003) offer to the mathematics community the fullest and most comprehensive reference to date for problem solving in the theory of modules and rings Nota de contenido: Free Modules, Projective, and Injective Modules -- Flat Modules and Homological Dimensions -- More Theory of Modules -- Rings of Quotients -- More Rings of Quotients -- Frobenius and Quasi-Frobenius Rings -- Matrix Rings, Categories of Modules and Morita Theory En línea: http://dx.doi.org/10.1007/978-0-387-48899-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34480 Ejemplares
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Título : Group Identities on Units and Symmetric Units of Group Rings Tipo de documento: documento electrónico Autores: Gregory T. Lee ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2010 Colección: Algebra and Applications, ISSN 1572-5553 num. 12 Número de páginas: XII, 196 p Il.: online resource ISBN/ISSN/DL: 978-1-84996-504-0 Idioma : Inglés (eng) Palabras clave: Mathematics Associative rings Rings (Algebra) Group theory and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest Nota de contenido: Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and En línea: http://dx.doi.org/10.1007/978-1-84996-504-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33656 Group Identities on Units and Symmetric Units of Group Rings [documento electrónico] / Gregory T. Lee ; SpringerLink (Online service) . - London : Springer London, 2010 . - XII, 196 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 12) .
ISBN : 978-1-84996-504-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Associative rings Rings (Algebra) Group theory and Algebras Theory Generalizations Clasificación: 51 Matemáticas Resumen: Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest Nota de contenido: Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of and En línea: http://dx.doi.org/10.1007/978-1-84996-504-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33656 Ejemplares
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