Publisher's Synopsis
Opening with an examination of the algebra of numbers, this text then proceeds to look at congruence classes (including;Clock Arithmetic), polynomials, binary operations and groups, and homomorphisms. An innovatory section on group actions (including applications to Sylow Theorems) precedes a discussion on abelian groups, free abelian groups, matrix reduction of generating sets, and the representation of f.g. abelian groups as products of cyclic groups. The final part deals with ring theory and includes coverage of axiomatic ring theory, Boolean rings and quotient rings before culminating with a glimpse into coding theory. The book as a whole provides a systematic approach which will lead the student through the area of abstract algebra and its uses in an easily assimilable way.
