ABSTRACT ALGEBRA, THIRD EDITION

Appropriate for undergraduate courses, this third edition has new chapters on Galois Theory and Module Theory, new solved problems and additional exercises in the chapters on group theory, boolean algebra and matrix theory. The text offers a systematic, well-planned, and elegant treatment of the main themes in abstract algebra. It begins with the fundamentals of set theory, basic algebraic structures such as groups and rings, and special classes of rings and domains, and then progresses to extension theory, vector space theory and finally the matrix theory. The boolean algebra by virtue of its relation to abstract algebra also finds a proper place in the development of the text. The students develop an understanding of all the essential results such as the Cayley’s theorem, the Lagrange’s theorem, and the Isomorphism theorem, in a rigorous and precise manner. Sufficient numbers of examples have been worked out in each chapter so that the students can grasp the concepts, the ideas, and the results of structure of algebraic objects in a comprehensive way. The chapter-end exercises are designed to enhance the student’s ability to further explore and interconnect various essential notions. Besides undergraduate students of mathematics, this text is equally useful for the postgraduate students of mathematics.