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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 : Algebra : Fields with Structure, Algebras and Advanced Topics Tipo de documento: documento electrónico Autores: Falko Lorenz ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Número de páginas: X, 340 p Il.: online resource ISBN/ISSN/DL: 978-0-387-72488-1 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Commutative algebra rings Field theory (Physics) Matrix Number Rings and Algebras Theory Polynomials Linear Multilinear 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, the Tsen rank 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: Ordered Fields and Real Fields -- Hilbert's Seventeenth Problem and the Real Nullstellensatz -- Orders and Quadratic Forms -- Absolute Values on Fields -- Residue Class Degree and Ramification Index -- Local Fields -- Witt Vectors -- The Tsen Rank of a Field -- Fundamentals of Modules -- Wedderburn Theory -- Crossed Products -- The Brauer Group of a Local Field -- Local Class Field Theory -- Semisimple Representations of Finite Groups -- The Schur Group of a Field En línea: http://dx.doi.org/10.1007/978-0-387-72488-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34169 Algebra : Fields with Structure, Algebras and Advanced Topics [documento electrónico] / Falko Lorenz ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - X, 340 p : online resource.
ISBN : 978-0-387-72488-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Commutative algebra rings Field theory (Physics) Matrix Number Rings and Algebras Theory Polynomials Linear Multilinear 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, the Tsen rank 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: Ordered Fields and Real Fields -- Hilbert's Seventeenth Problem and the Real Nullstellensatz -- Orders and Quadratic Forms -- Absolute Values on Fields -- Residue Class Degree and Ramification Index -- Local Fields -- Witt Vectors -- The Tsen Rank of a Field -- Fundamentals of Modules -- Wedderburn Theory -- Crossed Products -- The Brauer Group of a Local Field -- Local Class Field Theory -- Semisimple Representations of Finite Groups -- The Schur Group of a Field En línea: http://dx.doi.org/10.1007/978-0-387-72488-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34169 Ejemplares
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Título : Infinite Dimensional Algebras and Quantum Integrable Systems Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Petr P. Kulish ; Nenad Manojlovich ; Henning Samtleben Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2005 Colección: Progress in Mathematics num. 237 Número de páginas: VIII, 263 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7341-2 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Matrix theory Topological groups Lie System Physics Quantum physics Mathematical Methods in Groups, Groups Linear and Multilinear Algebras, Theory Systems Theory, Control Clasificación: 51 Matemáticas Resumen: This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV. International Congress on Mathematical Physics. Recent developments in the theory of infinite dimensional algebras and their applications to quantum integrable systems are reviewed by some of the leading experts in the field. The volume will be of interest to a broad audience from graduate students to researchers in mathematical physics and related fields. Contributors: E. Frenkel O.A. Castro-Alvaredo and A. Fring V.G. Kac and M. Wakimoto A. Gerasimov, S. Kharchev and D. Lebedev H.E. Boos, V.E. Korepin and F.A. Smirnov Kanehisa Takasaki Takashi Takebe L.A. Takhtajan and Lee-Peng Teo V. Tarasov Nota de contenido: Gaudin Model and Opers -- Integrable Models with Unstable Particles -- Quantum Reduction in the Twisted Case -- Representation Theory and Quantum Integrability -- Connecting Lattice and Relativistic Models via Conformal Field Theory -- Elliptic Spectral Parameter and Infinite-Dimensional Grassmann Variety -- Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. II -- Weil-Petersson Geometry of the Universal Teichmüller Space -- Duality for Knizhinik-Zamolodchikov and Dynamical Equations, and Hypergeometric Integrals En línea: http://dx.doi.org/10.1007/b137651 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35330 Infinite Dimensional Algebras and Quantum Integrable Systems [documento electrónico] / SpringerLink (Online service) ; Petr P. Kulish ; Nenad Manojlovich ; Henning Samtleben . - Basel : Birkhäuser Basel, 2005 . - VIII, 263 p : online resource. - (Progress in Mathematics; 237) .
ISBN : 978-3-7643-7341-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Matrix theory Topological groups Lie System Physics Quantum physics Mathematical Methods in Groups, Groups Linear and Multilinear Algebras, Theory Systems Theory, Control Clasificación: 51 Matemáticas Resumen: This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems'' held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV. International Congress on Mathematical Physics. Recent developments in the theory of infinite dimensional algebras and their applications to quantum integrable systems are reviewed by some of the leading experts in the field. The volume will be of interest to a broad audience from graduate students to researchers in mathematical physics and related fields. Contributors: E. Frenkel O.A. Castro-Alvaredo and A. Fring V.G. Kac and M. Wakimoto A. Gerasimov, S. Kharchev and D. Lebedev H.E. Boos, V.E. Korepin and F.A. Smirnov Kanehisa Takasaki Takashi Takebe L.A. Takhtajan and Lee-Peng Teo V. Tarasov Nota de contenido: Gaudin Model and Opers -- Integrable Models with Unstable Particles -- Quantum Reduction in the Twisted Case -- Representation Theory and Quantum Integrability -- Connecting Lattice and Relativistic Models via Conformal Field Theory -- Elliptic Spectral Parameter and Infinite-Dimensional Grassmann Variety -- Trigonometric Degeneration and Orbifold Wess-Zumino-Witten Model. II -- Weil-Petersson Geometry of the Universal Teichmüller Space -- Duality for Knizhinik-Zamolodchikov and Dynamical Equations, and Hypergeometric Integrals En línea: http://dx.doi.org/10.1007/b137651 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35330 Ejemplares
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Título : Positive Linear Maps of Operator Algebras Tipo de documento: documento electrónico Autores: Erling Størmer ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: VIII, 136 p Il.: online resource ISBN/ISSN/DL: 978-3-642-34369-8 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Functional analysis Physics Analysis Linear and Multilinear Algebras, Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout. Nota de contenido: Introduction -- 1 Generalities for positive maps -- 2 Jordan algebras and projection maps -- 3 Extremal positive maps -- 4 Choi matrices and dual functionals -- 5 Mapping cones -- 6 Dual cones -- 7 States and positive maps -- 8 Norms of positive maps -- Appendix: A.1 Topologies on B(H) -- A.2 Tensor products -- A.3 An extension theorem -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-34369-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32550 Positive Linear Maps of Operator Algebras [documento electrónico] / Erling Størmer ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013 . - VIII, 136 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-3-642-34369-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Functional analysis Physics Analysis Linear and Multilinear Algebras, Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory. The author, a leading authority on the subject, sets out numerous results previously unpublished in book form. In addition to outlining the properties and structures of positive linear maps of operator algebras into the bounded operators on a Hilbert space, he guides readers through proofs of the Stinespring theorem and its applications to inequalities for positive maps. The text examines the maps’ positivity properties, as well as their associated linear functionals together with their density operators. It features special sections on extremal positive maps and Choi matrices. In sum, this is a vital publication that covers a full spectrum of matters relating to positive linear maps, of which a large proportion is relevant and applicable to today’s quantum information theory. The latter sections of the book present the material in finite dimensions, while the text as a whole appeals to a wider and more general readership by keeping the mathematics as elementary as possible throughout. Nota de contenido: Introduction -- 1 Generalities for positive maps -- 2 Jordan algebras and projection maps -- 3 Extremal positive maps -- 4 Choi matrices and dual functionals -- 5 Mapping cones -- 6 Dual cones -- 7 States and positive maps -- 8 Norms of positive maps -- Appendix: A.1 Topologies on B(H) -- A.2 Tensor products -- A.3 An extension theorem -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-642-34369-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32550 Ejemplares
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Título : Advanced Linear Algebra Tipo de documento: documento electrónico Autores: Steven Roman ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 135 Número de páginas: XVIII, 526 p Il.: online resource ISBN/ISSN/DL: 978-0-387-72831-5 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviews of the second edition: "In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields...the exercises are rewritten and expanded....Overall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book." Ali-Akbar Jafarian, ZentralblattMATH "This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints given for the solution of trickier problems...It represents linear algebra and does so comprehensively." Henry Ricardo, MAA Online Nota de contenido: Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- Topics -- Metric Vector Spaces: The Theory of Bilinear Forms -- Metric Spaces -- Hilbert Spaces -- Tensor Products -- Positive Solutions to Linear Systems: Convexity and Separation -- Affine Geometry -- Singular Values and the Moore–Penrose Inverse -- An Introduction to Algebras -- The Umbral Calculus En línea: http://dx.doi.org/10.1007/978-0-387-72831-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34171 Advanced Linear Algebra [documento electrónico] / Steven Roman ; SpringerLink (Online service) . - New York, NY : Springer New York, 2008 . - XVIII, 526 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 135) .
ISBN : 978-0-387-72831-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra. From the reviews of the second edition: "In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields...the exercises are rewritten and expanded....Overall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book." Ali-Akbar Jafarian, ZentralblattMATH "This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints given for the solution of trickier problems...It represents linear algebra and does so comprehensively." Henry Ricardo, MAA Online Nota de contenido: Basic Linear Algebra -- Vector Spaces -- Linear Transformations -- The Isomorphism Theorems -- Modules I: Basic Properties -- Modules II: Free and Noetherian Modules -- Modules over a Principal Ideal Domain -- The Structure of a Linear Operator -- Eigenvalues and Eigenvectors -- Real and Complex Inner Product Spaces -- Structure Theory for Normal Operators -- Topics -- Metric Vector Spaces: The Theory of Bilinear Forms -- Metric Spaces -- Hilbert Spaces -- Tensor Products -- Positive Solutions to Linear Systems: Convexity and Separation -- Affine Geometry -- Singular Values and the Moore–Penrose Inverse -- An Introduction to Algebras -- The Umbral Calculus En línea: http://dx.doi.org/10.1007/978-0-387-72831-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34171 Ejemplares
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