Description
Book Synopsis
The main theme in classical ring theory is the structure theory of rings of a particular kind. For example, no one text book in ring theory could miss the Wedderburn-Artin theorem, which says that a ring R is semisimple Artinian iffR is isomorphic to a finite direct sum of full matrix rings over skew fields.
Table of Contents
Introduction. 1. Basic Notions. 2. Finitely Presented Modules over Serial Rings. 3. Prime Ideals in Serial Rings. 4. Classical Localizations in Serial Rings. 5. Serial Rings with the A.C.C. on annihilators and Nonsingular Serial Rings. 6. Serial Prime Goldie Rings. 7. Noetherian Serial Rings. 8. Artinian Serial Rings. 9. Serial Rings with Krull Dimension. 10. Model Theory for Modules. 11. Indecomposable Pure Injective Modules over Serial Rings. 12. Super-Decomposable Pure Injective Modules over Commutative Valuation Rings. 13. Pure Injective Modules over Commutative Valuation Domains. 14. Pure Projective Modules over Nearly Simple Uniserial Domains. 15. Pure Projective Modules over Exceptional Uniserial Rings. 16. Sigma-Pure Injective Modules over Serial Rings. 17. Endomorphism Rings of Artinian Modules. Bibliography. Notations. Index.
