Modules and Rings

This Book On Modern And Non-commutative Ring Theory Is Ideal For Beginning Graduate Students. It Starts At The Foundations Of The Subject And Progresses Rapidly Through The Basic Concepts To Help The Reader Reach Current Research Frontiers. Students Will Have The Chance To Develop Proofs, Solve Problems, And To Find Interesting Questions. The First Half Of The Book Is Concerned With Free, Projective And Injective Modules, Tensor Algebras, Simple Modules And Primitive Rings, The Jacobson Radical, And Subdirect Products. Later In The Book, More Advanced Topics, Such As Hereditary Rings, Categories And Functors, Flat Modules And Purity Are Introduced. These Later Chapters Will Also Prove A Useful Reference For Researchers In Non-commutative Ring Theory. Enough Background Material (including Detailed Proofs) Is Supplied To Give The Student A Firm Grounding In The Subject. Modules -- Free Modules -- Injective Modules -- Tensor Products -- Certain Important Algebras -- Simple Modules And Primitive Rings -- The Jacobson Radical -- Subdirect Product Decompositions -- Primes And Semiprimes -- Projective Modules And More On Wedderburn Theorems -- Direct Sum Decompositions -- Simple Algebras -- Hereditary Rings, Free And Projective Modules -- Module Constructions -- Categories And Functors -- Module Categories -- Flat Modules -- Purity. John Dauns. Includes Bibliographical References (p. 432-435) And Indexes. This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject. An ideal book on module and non-commutative ring theory for graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers.