Algebras, Rings and Modules

Abstract

This updated and revised edition of Algebras, Rings and Modules providesthe classical aspects of the theory of groups and their representations,as well as a general introduction to the modern theory of representationsincluding the representations of quivers and finite partially orderedsets and their applications to finite dimensional algebras.Detailed attention is given in the Second Edition to special classesof algebras and rings including Frobenius, quasi-Frobenius, rightserial rings and tiled orders using the technique of quivers. Themost important recent developments in the theory of these rings areexamined.The book examines the Cartan Determinant Conjecture, and also givessome properties of global dimensions of different classes of rings.The final chapters of this volume explore the theory of semiprimeNoetherian semiperfect and semidistributive rings.This book is mainly written for researchers in the theory of ringsand algebras, but graduate and postgraduate students, especiallythose using algebraic techniques, will find this book of interest.