ADVANCED MODERN ALGEBRA

This book's organizing principle is the interplaybetween groups and rings, where 'rings' includes the ideasof modules. It contains basic definitions, complete and clear theorems(the first with brief sketches of proofs), and gives attention tothe topics of algebraic geometry, computers, homology, andrepresentations. More than merely a succession of definition-theorem-proofs,this text put results and ideas in context so that students can appreciatewhy a certain topic is being studied, and where definitions originate. Chapter topics include groups; commutative rings;modules; principal ideal domains; algebras; cohomology and representations;and homological algebra. For individuals interestedin a self-study guide to learning advanced algebra and its related topics.