A Course On Abstract Algebra
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A Course on Abstract Algebra
This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the author's lecture notes at the Department of Mathematics, National Chung Cheng University of Taiwan, it begins with a description of the algebraic structures of the ring and field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's Theorem and Sylow's Theorems follow as applications of group theory. Ring theory forms the second part of abstract algebra, with the ring of polynomials and the matrix ring as basic examples. The general theory of ideals as well as maximal ideals in the rings of polynomials over the rational numbers are also discussed. The final part of the book focuses on field theory, field extensions and then Galois theory to illustrate the correspondence between the Galois groups and field extensions. This textbook is more accessible and less ambitious than most existing books covering the same subject. Readers will also find the pedagogical material very useful in enhancing the teaching and learning of abstract algebra.
A Course in Abstract Algebra, 4th Edition
Author: V.K. Khanna & S.K Bhamri
language: en
Publisher: Vikas Publishing House
Release Date:
Designed for undergraduate and postgraduate 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 (Linear Algebra) and fields. The topics under Groups include subgroups, permutation groups, finite abelian groups, Sylow theorems, direct products, group actions, solvable and nilpotent groups. The course in Ring theory covers ideals, embedding of rings, euclidean domains, PIDs, UFDs, polynomial rings, irreducibility criteria, Noetherian 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 and 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 also plenty of scope for the readers to try and solve problems on their own. NEW IN THIS EDITION • Learning Objectives and Summary with each chapter • A large number of additional worked-out problems and examples • Alternate proofs of some theorems and lemmas • Reshuffling/Rewriting of certain portions to make them more reader friendly
A Course in Abstract Algebra, 5th Edition
Author: Khanna V.K. & Bhamri S.K
language: en
Publisher: Vikas Publishing House
Release Date: 2016
Designed for undergraduate and postgraduate 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, Fields and Linear Algebra. The topics under groups include subgroups, finitely generated abelian groups, group actions, solvable and nilpotent groups. The course in ring theory covers ideals, embedding of rings, Euclidean domains, PIDs, UFDs, polynomial rings, Noetherian (Artinian) rings. Topics of field include algebraic extensions, splitting fields, normal extensions, separable extensions, algebraically closed fields, Galois extensions, and construction by ruler and compass. The portion on linear algebra deals with vector spaces, linear transformations, Eigen spaces, diagonalizable operators, inner product spaces, dual spaces, operators on inner product spaces etc. The theory has been strongly supported by numerous examples and worked-out problems. There is also plenty of scope for the readers to try and solve problems on their own. New in this Edition • A full section on operators in inner product spaces. • Complete survey of finite groups of order up to 15 and Wedderburn theorem on finite division rings. • Addition of around one hundred new worked-out problems and examples. • Alternate and simpler proofs of some results. • A new section on quick recall of various useful results at the end of the book to facilitate the reader to get instant answers to tricky questions.