Serial Rings

ISBN-13: 9789401038621 / Angielski / Miękka / 2012 / 226 str.

Gennadi Puninski

Opis

This book presents an exhaustive and up-to-date overview of the structure theory of serial rings, and the various methods of treating them. Results have been scattered throughout the literature, and the achievements of some schools, such as the Kiev school, seem little-known. This volume endeavours to unify the wide spectrum of tools used in this area and state the theory of serial rings based on two constructions: firstly, localisation with respect to a semi-prime Goldie ideal; and, secondly, a hidden 'blow-up' construction in a serial ring. Part of the work deals with the theory of modules over a serial ring, especially with finitely presented and pure injective modules. Other topics include noetherian serial rings and Artinian serial rings. Audience: This volume can be used as a textbook in ring theory and in the model theory of modules, and will also be of interest to postgraduates and researchers whose work involves rings and algebras.

Spis treści

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.