| Author: | P. B. Bhattacharya, S. K. Jain & S. R. Nagpaul |
| Release at: | 1994 |
| Pages: | 507 |
| Edition: | 2nd Edition |
| File Size: | 8 MB |
| File Type: | |
| 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
Part V Additional topics
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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