Abstract Algebra

Informationen zum Autor David S. Dummit and Richard M. Foote are the authors of Abstract Algebra, 3rd Edition, published by Wiley. Klappentext Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.* The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible. Zusammenfassung Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. Inhaltsverzeichnis PreliminariesPart I Group Theory* Introduction to Groups* Subgroups* Quotient Groups and Homomorphisms* Group Actions* Direct and Semidirect Products and Abelian Groups* Further Topics in Group TheoryPart II Ring Theory* Introduction to Rings* Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains* Polynomial RingsPart III Modules and Vector Spaces* Introduction to Module Theory* Vector Spaces* Modules over Principal Ideal DomainsPart IV Field Theory and Galois Theory* Field Theory* Galois TheoryPart V An Introduction To Commutative Rings, Algabraic Geometry, and Homological Algebra* Commutative Rings and Algebraic Geometry* Artinian Rings, Discrete Valuation Rings, and Dedekind Domains* Introduction to Homological Algebra and Group CohomologyPart IV Introduction To The Representation Theory of Finite Groups* Representation Theory and Character Theory* Examples and Applications of Character TheoryAppendix I Cartesian Products and Zorn's LemmaAppendix II Category Theory Index...

Klappentext
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. * The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible.

Inhalt
Preliminaries Part I Group Theory * Introduction to Groups * Subgroups * Quotient Groups and Homomorphisms * Group Actions * Direct and Semidirect Products and Abelian Groups * Further Topics in Group Theory Part II Ring Theory * Introduction to Rings * Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains * Polynomial Rings Part III Modules and Vector Spaces * Introduction to Module Theory * Vector Spaces * Modules over Principal Ideal Domains Part IV Field Theory and Galois Theory * Field Theory * Galois Theory Part V An Introduction To Commutative Rings, Algabraic Geometry, and Homological Algebra * Commutative Rings and Algebraic Geometry * Artinian Rings, Discrete Valuation Rings, and Dedekind Domains * Introduction to Homological Algebra and Group Cohomology Part IV Introduction To The Representation Theory of Finite Groups * Representation Theory and Character Theory * Examples and Applications of Character Theory Appendix I Cartesian Products and Zorn's Lemma Appendix II Category Theory Index

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