Algebraic Structures - Ellis Horwood Series Mathematics & Its Applications.

This book completes the coverage of abstract algebra initiated by the author's "Modern Algebra" in 1981.;This companion volume commences with a treatment of groups, rings and fields, completing the basic course begun in the previous book by providing applications to other disciplines. The treatment becomes concrete and computational, including a short discussion of some important simple groups and a matrix theoretical introduction to the representation theory of finite groups. This approach, more straightforward for intending specialists than the abstract approach through modules, should make the concepts accessible to physicists, chemists and other scientists wishing to apply the theory in their work. The computational approach to linear groups and the use of computers in abstract mathematics, a feature of increasing importance, provides one of the first expositions at this level.;The reader is involved in providing proofs and in working out problems not fully solved in the text. Other problems suggest themselves as progress is made, particularly in the latter section of the book, where active involvement increases, with exercises being provided at the end of each chapter.