Basic Abstract Algebra
2nd Edition
Published on 25. November 1994
Book
Paperback/Softback
508 pages
978-0-521-46629-5 (ISBN)
Description
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.
Reviews / Votes
"...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 ScientistMore details
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Edition type
Revised edition
Product notice
Paperback (trade)
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 30 mm
Weight
817 gr
ISBN-13
978-0-521-46629-5 (9780521466295)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Previous edition
P. B. Bhattacharya
Basic Abstract Algebra
Book
04/1986
Cambridge University Press
€30.95
Article exhausted; check for reprint
Content
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.