A COURSE IN ABSTRACT ALGEBRA, Fourth edition, VIJAY K KHANNA, S. K. BHAMBRI
The main text can be divided into 4 section on Group, Rings, Vector Spaces (linear algebra) and fields. Fairly sufficient ground has covered in the first 3 sections. It is only in the last section on Fields that we can possibly be accused of being stingy. But then there are constraints and it was paucity of space and time that finally made us keep Galois theory out. Maybe in a subsequent me edition it would find its way in.
Different concepts have been explained with the help of examples. A large number of problems and solutions have been provided to assist one a firm grip on the ideas developed. There is plenty of scope for the reader to try and solve problems on his own. In all, a substantial variety of challenges is assured.
We deeply indebted to all those authors whose books (research papers) on Algebra influenced our learning of the subject and take this opportunity to express our sincere gratitude to them We are also thankful to those friends and colleagues with whom we had fruitful discussions from time to time.
Topics discussed in this book are,
1. Preliminaries
2.Groups
3. Normal subgroup, Homomorphism, Permutation Groups
4. Automorphism and Conjugate Elements
5.Sylo Theorems and Direct products
6.Group Actions, Solvable and Nilpotent Groups
7.Rings
8. Homomorphism and Embedded Rings
9. Euclidean and Factorization domain
10. Vector Spaces
11. Linear Transformations
12. EIGEN Values and EIGEN Vectors
13. Fields
14.More on Fields
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