Abstract Algebra
(Sprache: Englisch)
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,...
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Klappentext zu „Abstract Algebra “
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.
Inhaltsverzeichnis zu „Abstract Algebra “
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 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
Bibliographische Angaben
- Autoren: David S. Dummit , Richard M. Foote
- 2006, 3. Aufl., 944 Seiten, Maße: 19,5 x 24,1 cm, Gebunden, Englisch
- Verlag: Wiley & Sons
- ISBN-10: 0471433349
- ISBN-13: 9780471433347
Sprache:
Englisch
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