A Course in Abstract Algebra

 
9780706965704: A Course in Abstract Algebra
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ABOUT THE BOOK
Designed for undergraduate and post graduate students of mathematics, the book can also be used by those preparing for various competitive examinations. The text starts with a brief introduction to results from Set Theory and Number Theory. It then goes on to cover Groups, Rings, Vector spaces and Fields. The topics under Groups include Subgroups, Normal subgroups, Finitely generated abelian groups, Group actions, Solvable and Nilpotent groups. The course in Ring Theory covers Ideas, Imbedding of rings, Euclidean domains, Principal ideal domains, Unique factorization domains, Polynomial rings, Noetherian (Artinian) rings. The section on Vector spaces deals with Linear transformations, Inner product spaces, Dual spaces, Eigen spaces, Diagonalizable operators etc. Under Fields, Algebraic extensions, Splitting fields, Normal extensions, Separable extensions, Algebraically closed fields, Galois extensions and construction by ruler and compass are discussed. The theory has been strongly supported by numerous examples and worked out problems. There is plenty of scope also for the reader to try and solve problems on his (her) own.
SALIENT FEATURES
New in the Third Edition:

A full new chapter on Groups
Revamping of the chapter on Eigen Values to make it more reader-friendly
Splitting of the chapter on Fields for a focused approach.
CONTENTS
Preliminaries.
Groups.
Normal Subgroups.
Homomorphisms.
Permutation Groups.
Automorphisms and Conjugate Elements.
Sylow Theorems and Direct Products.
Group Actions, Solvable and Nilpotent Groups.
Rings
Homomorphisms and Imbedding of Rings.
Euclidean and Factorization Domains.
Vector Spaces.
Linear Transformations.
Eigen Values and Eigen Vectors
Fields
More on Fields
Index
About The Author
Vijay K Khanna is Reader in Deptt. of Mathematics, Kirori Mal College, University of Delhi and has been teaching undergraduate and postgraduate students for over 35 years. His other publications include Lattices and Boolean Algebras, Solid Geometry, and Business Mathematics published by Vikas.
S K Bhambri is Reader in Deptt. of Mathematics, Kirori Mal College, University of Delhi and has been teaching undergraduate and postgraduate students for over 35 years. He got his doctorate in 1981 from London. He is co-author of Business Mathematics, published by Vikas.

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