A comprehensive introduction to the homological and structural methods of ring theory and related topics, this book includes original results as well as the most recent work in the field. It is unique in that it concentrates on distributive modules and rings, an area in which the author is recognized as one of the world's leading experts.
A module is said to be distributive if the lattice of its submodules is distributive. Distributive rings are exemplified by factor rings of direct products of division rings, commutative semihereditary rings, and uniserial rings. Direct sums of distributive modules are studied in detail, as well as relations with flat modules and modules whose endomorphisms could be extended or lifted.
Starting from a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. A number of exercises are also included to give further insight into the topics covered and to draw attention to relevant results in the literature. This detailed and comprehensive book will be an invaluable source of reference to researchers and specialists in this area.
Table of Contents
1. Projective and Injective Modules 2. Bezout and Regular Modules 3. Continuous and Finite-Dimensional Modules 4. Classical Localizations 5. Flat Modules and Semiperfect Rings 6. Semihereditary Rings 7. Endomorphism Rings and Distributivity 8. Q max (A) and Nonsingular Rings 9. Polynomials, Series and Quaternions 10.
Semidistributive Rings and Modules 11. Distributive Group and Monoid Rings 11. Rings Related to Commutative Rings 12. Self-injective and Skew-injective Rings 13. Radicals, Local and Semisimple Modules 14. Rings with Maximun Conditions