Abstract algebra

By: Dummit, David StevenContributor(s): Foote, Richard MMaterial type: TextTextPublication details: New Delhi: John Wiley, 2004Edition: 3rd EditionDescription: xii, 932 pagesISBN: 9788126532285Subject(s): Algebra, AbstractDDC classification: 512.02
Contents:
Part. 1. 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 2. Ring theory: Introduction to rings -- Euclidean domains, principal ideal domains and unique factorization domains -- Polynomial rings -- Part 3. Modules and vector spaces: Introduction to module theory -- Vector spaces -- Modules over principal ideal domains -- Part. 4. Field theory and Galois theory: Field theory -- Galois theory -- Part 5. An introduction to commutative rings, algebraic 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 6. Introduction to the representation theory of finite groups: Representation theory and character theory -- Examples and applications of character theory.
Summary: 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.
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Includes index

Part. 1. 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 2. Ring theory: Introduction to rings --
Euclidean domains, principal ideal domains and unique factorization domains --
Polynomial rings --
Part 3. Modules and vector spaces: Introduction to module theory --
Vector spaces --
Modules over principal ideal domains --
Part. 4. Field theory and Galois theory: Field theory --
Galois theory --
Part 5. An introduction to commutative rings, algebraic 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 6. Introduction to the representation theory of finite groups: Representation theory and character theory --
Examples and applications of character theory.

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.

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