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Basic Abstract Algebra PB Bhattacharya SK Jain SR Nagpaul [PDF]

### Algebra (2nd Edition) by Michael Artin

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Algebra (2nd Edition) written by Michael Artin .
This book will get you there if you believe in it. It has examples with solutions and problems with solutions. The only topic that does not have problems with solutions is categories. For this, I have the Hungerford text, and I am presently in the process of finding a better book for this. Otherwise it is the perfect book for self-study. This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants. The second part deals with groups. The third part treats rings and modules. The fourth part is concerned with field theory. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra. The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedderburn-Artin theorem for semisimple artinian rings, Noether-Lasker theorem, the Smith-Normal form over a PID, finitely generated modules over a PID and their applications to rational and Jordan canonical forms and the tensor products of modules. Throughout, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises. In addition, the book contains many examples fully worked out and a variety of problems for practice and challenge. Solution to the odd-numbered problems are provided at the end of the book to encourage the student in problem solving. This new edition contains an introduction to categories and functors, a new chapter on tensor products and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples.

Book Detail :-
Title: Basic Abstract Algebra
Edition: Second Edition
Author(s): P. B. Bhattacharya, S. K. Jain, S. R. Nagpaul
Publisher: Cambridge University Press
Series:
Year: 1994
Pages: 509
Type: PDF
Language: Englsih
ISBN: 0521466296,9780521466295
Country: India
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Author P. B. Bhattacharya (1923–1988) was a mathematician, he was appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
, University of Delhi, India

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Book Contents :-
Algebra (2nd Edition) written by Michael Artin . cover the following topics.

• 1. Matrices
2. Groups
3. Vector Spaces
4. Linear Operators
5. Applications of Linear Operators
6. Symmetry
7. More Group Theory
8. Bilinear Forms
9. Linear Groups
10. Group Representations
11. Rings
12. Factoring
13. Quadratic Number Fields
14. Linear Algebra in a Ring
15. Fields
16. Galois Theory
Exercises

• Note:-

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