A Course in Ring Theory

Originally a Chelsea Publishing imprint, this new AMS edition contains the core material for an undergraduate first course in ring theory. Using the underlying theme of projective and injective modules, the author touches upon various aspects of commutative and noncommutative ring theory. A number of major results are highlighted and proved. The book contains numerous exercises and a list of suggested additional reading. Part I, .Projective Modules., begins with basic module theory and then proceeds to surveying various special classes of rings. Part II, .Polynomial Rings., focuses on the study of these rings in a mildly noncommutative setting. Part III, .Injective Modules., includes various notions of the ring of quotients, the Goldie Theorems, and the characterization of the injective modules over Noetherian rings.