Introductory Lectures on Rings and Modules

The focus of this book is the study of the noncommutative aspects of rings and modules, and the style will make it accessible to anyone with a background in basic abstract algebra. Features of interest include an early introduction of projective and injective modules; a module theoretic approach to the Jacobson radical and the Artin-Wedderburn theorem; the use of Baer’s criterion for injectivity to prove the structure theorem for finitely generated modules over a principal ideal domain; and applications of the general theory to the representation theory of finite groups. Optional material includes a section on modules over the Weyl algebras and a section on Goldie’s theorem. When compared to other more encyclopedic texts, the sharp focus of this book accommodates students meeting this material for the first time. It can be used as a first-year graduate text or as a reference for advanced undergraduates.