Basic Abstract Algebra: Second Edtionby: P.B. Bhattacharya, S.K. Jain, S.R.Nagpaul,
This text on abstract algebra for undergraduate students is self-contained and gives complete and comprehensive coverage of the topics usually taught at this level, providing flexibility in the section of topics to be taught in individual classes. All the topics are discussed in a direct and detailed manner. The book is divided into five parts. […]
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This text on abstract algebra for undergraduate students is self-contained and gives complete and comprehensive coverage of the topics usually taught at this level, providing flexibility in the section of topics to be taught in individual classes. All the topics are discussed in a direct and detailed manner.
The book is divided into five parts. the first part contains all the fundamental information necessary for using the remainder of the book: information introduction to sets, number systems, matrices, and determinate. The second parts deals with groups. Starting with group axioms, the topics discussed include G-sets, the Jordan Holder theorems, simplicity of An and nonavailability of Sn, n>4, the fundamental theorem of finitely generated abelian groups, and Sylow theorem. The third part treats rings and rings and modules, including prime and maximal ideals, UFD, PID, ring of fractions of a commutative ring with respect to a multiplicative set, systematic development of integers from Peano’s axioms, vector spaces, completely reducible modules, and rank. The fourth part is concerned with field theory: algebraic extensions, of a field, algebraically closed fields, normal and separable extensions, and the fundamental theorem of Galois theory. All these are treated with numerous examples worked out. Much of the material in parts II, III, and IV forms the core syllabus of a course in abstract algebra, The fifth part goes on to treat some additional topics not usually taught at the undergraduate level, such as the Wedder bum-Ar tin theorem for semi-simple artinian rings, the noether-Lasker theorem, the Smith normal from over a PID and their applications to rational and Jordan canonical forms, and tensor products of modules.
Throughout he text, complete proofs have been given for all theorems without glossing over significant details or leaving important theorems as exercises.In addition, he book contains many examples fully worked out and a variety of problems or practice an challenge. Solutions to the odd numbered problems are provided at the end of the book.
This new edition contains an introduction to categories and functors, a new chapter on tensor products, and a discussion of the new (1993) approach to the celebrated Noether-Lasker theorem. In addition, there are over 150 new problems and examples particularly aimed at relating abstract concepts to concrete situations.
“A through and surprising clean-cut survey of the group/ring/field/ troika which manages o convey he idea of algebra as a unified enterprise.”
Publisher: CAMBRIDGE UNIVERSITY PRESS
Publish Date: 1995
Page Count: 487