Basic Abstract Algebra

This book provides a complete abstract algebra course, enabling instructors to select the topics for use in individual classes.

P. B. Bhattacharya (Author), S. K. Jain (Author), S. R. Nagpaul (Author)

9780521466295, Cambridge University Press

Paperback, published 25 November 1994

508 pages
23.6 x 15.4 x 3.4 cm, 0.82 kg

"...a thorough and surprisingly clean-cut survey of the group/ring/field troika which manages to convey the idea of algebra as a unified enterprise." Ian Stewart, New Scientist

This book represents a complete course in abstract algebra, providing instructors with flexibility in the selection of topics to be taught in individual classes. All the topics presented are discussed in a direct and detailed manner. Throughout the text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. The book contains many examples fully worked out and a variety of problems for practice and challenge. Solutions to the odd-numbered problems are provided at the end of the book. This new edition contains an introduction to lattices, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Lasker–Noether theorem. In addition, there are over 100 new problems and examples, particularly aimed at relating abstract concepts to concrete situations.

Preface to the second edition
Preface to the first edition
Glossary of symbols
Part I. Preliminaries: 1. Sets and mappings
2. Integers, real numbers, and complex numbers
3. Matrices and determinants
Part II. Groups: 4. Groups
5. Normal subgroups
6. Normal series
7. Permutation groups
8. Structure theorems of groups
Part III. Rings and Modules: 9. Rings
10. Ideals and homomorphisms
11. Unique factorization domains and euclidean domains
12. Rings of fractions
13. Integers
14. Modules and vector spaces
Part IV. Field Theory: 15. Algebraic extensions of fields
16. Normal and separable extensions
17. Galois theory
18. Applications of Galios theory to classical problems
Part V. Additional Topics: 19. Noetherian and Artinian modules and rings
20. Smith normal form over a PID and rank
21. Finitely generated modules over a PID
22. Tensor products
Solutions to odd-numbered problems
Selected bibliography
Index.

Subject Areas: Algebra [PBF]