Groups, Rings and Modules with Applications

This book is an exposition of some fundamental concepts of algebra coupled with recent developments in related topics. The reader is not assumed to have any prior knowledge of set theory and abstract algebra. Particular emphasis has been laid on naturality. The book is meant for undergraduate and postgraduate courses in abstract algebra as well as for students and researchers in mathematics, mathematical sciences and computer science. The coverage includes semigroups, groups, rings, modules and their applications to geometry, topology, and theoretical computer science. A brief discussion of autometrized algebra, fuzzy algebra, algebraic geometry, algebraic topology and category theory has also been included. An appendix on the history of the development of abstract algebra is incorporated. Each chapter consists of definitions, theorems, proofs, and corollaries with numerous examples and worked out exercises illustrating the concepts and providing problem-solving techniques.