ABSTRACT ALGEBRA

PHI Learning Pvt. Ltd., Jan 1, 2005 - Mathematics - 372 pages
Appropriate for undergraduate courses, this second edition has a new chapter on lattice theory, many revisions, 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 inter-connect various essential notions.

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Contents

 GROUPTHEORY 41103 41 EXTENSION THEORY 141153 141 LATTICE THEORY 154166 154 BOOLEANALGEBRA 167194 167
 VECTOR SPACE THEORY 195244 195 MATRK THEORY 245348 245 Bibliography 349 Copyright

Popular passages

Page 10 - The cartesian product A x В of two sets A and В is defined as the set of all ordered pairs (x, y), where xe A and ye В.
Page 5 - SETS Two sets A and В are said to be disjoint if no element of A is in В and no element of В is in A.