# Basic Abstract Algebra 2nd Edition (PDF)

 Author: P. B. Bhattacharya, S. K. Jain & S. R. Nagpaul Release at: 1994 Pages: 507 Edition: 2nd Edition File Size: 8 MB File Type: PDF Language: English

#### Description of Basic Abstract Algebra 2nd Edition (PDF)

Basic Abstract Algebra 2nd Edition by P. B. Bhattacharya, S. K. Jain & S. R. Nagpaul is a great Mathematics book available in (eBook) PDF download. More than 150 new problems and examples have been added. The new problems include several that relate abstract concepts to concrete situations. Among others, we present applications of G-sets, the division algorithm and greatest common divisors in a given euclidean domain. In particular. we should mention the combinatorial applications of the Burnside theorem to real. life problems. A proof for the constructibility of a regular n-gon has been included in Chapter 18.

We have included a recent elegant and elementary proof, due to Osofsky, of the celebrated Noether—Lasker theorem. Chapter 22 on tensor products with an introduction to categories and functors is a new addition to Part IV. This chapter provides basic results on tensor products that are useful and important in present-day mathematics.

We are pleased to thank all of the professors and students in the many universities who used this textbook during the past seven years and contributed their useful feedback. In particular, we would like to thank Sergio R. Lopez-Permouth for his help during the time when the revised edition was being prepared. Finally, we would like to acknowledge the staff of Cambridge University Press for their help in bringing out this second edition so efficiently.

#### Content of Basic Abstract Algebra 2nd Edition (PDF)

Part I Preliminaries

Chapter 1: Sets and mappings

Chapter 2: Integers, real numbers, and complex numbers

Chapter 3: Matrices and determinants

Part II Groups

Chapter 4: Groups

Chapter 5: Normal subgroups

Chapter 6: Normal series

Chapter 7: Permutation groups

Chapter 8: Structure theorems of groups

Part III Rings and modules

Chapter 9: Rings

Chapter 10: Ideals and homomorphisms

Chapter 11: Unique factorization domains and euclidean domains

Chapter 12: Rings of fractions

Chapter 13: Integers

Chapter 14: Modules and vector spaces

Part IV Field theory

Chapter 15: Algebraic extensions of fields

Chapter 16: Normal and separable extensions

Chapter 17: Galois theory

Chapter 18: Applications of Galois theory to classical problems

Chapter 19: Noetherian and artinian modules and rings

Chapter 20: Smith normal form over a PID and rank

Chapter 21: Finitely generated modules over a PID

Chapter 22: Tensor products

Solutions to odd-numbered problems

Selected bibliography

Index

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