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About this book :-
Abstract Algebra (3E) written by David S. Dummit and Richard M. Foote .
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 student's understanding. The text book is designed for a full-year introduction to abstract algebra at the advanced undergraduate or graduate level, but contains substantially more material than would normally be covered in one year. Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, group theory, ring theory etc.
Book Detail :-
Title: Abstract Algebra
Edition: Third Edition
Author(s): David S. Dummit, Richard M. Foote
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About Author :-
The author David Steven Dummit is a professor in the Mathematics department at University of Vermont
The author Richard M. Foote Department of Mathematics & Statistics, Professor Emeritus. Areas of Expertise and/or Research. Group theory and applications, algebraic number theory.
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• Download PDF Abstract Algebra (3E) by David Dummit and Richard Foote
• Download PDF Abstract Algebra (3E Solution) by David Dummit and Richard Foote
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Book Contents :-
Abstract Algebra (3E) written by David S. Dummit and Richard M. Foote . cover the following topics.
Part 1 - GROUP THEORY
1. Introduction to Groups
3. Quotient Groups and Homomorphisms
4. Group Actions
5. Direct and Semidirect Products and Abelian Groups
6. Further Topics in Group Theory
Part II - RING THEORY
7. Introduction to Rings
8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
9. Polynomial Rings
Part III - MODULES AN D VECTOR SPACES
10. Introduction to Module Theory
11. Vector Spaces
12. Modules over Principal Ideal Domains
Part IV - FIELD THEORY AND GALOIS THEORY
13. Field Theory
14. Galois Theory
Part V - AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOM ETRY, AND HOMOLOGICAL ALGEBRA
15. Commutative Rings and Algebraic Geometry
16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
17. Introduction to Homological Algebra and Group Cohomology
Part VI - INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS
18. Representation Theory and Character Theory
19. Examples and Applications of Character Theory
Appendix 1: Cartesian Products and Zorn's Lemma
Appendix II: Category Theory
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