Synopses & Reviews
This monograph first published in 1986 is a reasonably self-contained account of a large part of the theory of non-commutative Noetherian rings. The author focuses on two important aspects: localization and the structure of infective modules. The former is presented in the opening chapters after which some new module-theoretic concepts and methods are used to formulate a new view of localization. This view, which is one of the book's highlights, shows that the study of localization is inextricably linked to the study of certain injectives and leads, for the first time, to some genuine applications of localization in the study of Noetherian rings. In the last part Professor Jategaonkar introduces a unified setting for four intensively studied classes of Noetherian rings: HNP rings, PI rings, enveloping algebras of solvable Lie algebras, and group rings of polycyclic groups. Some appendices summarize relevant background information about these four classes.
Table of Contents
1. Ore's method of localizatiohn; 2. Orders in semi-simple rings; 3. Localization at semi-prime ideals; 4. Localization, primary decomposition, and the second layer; 5. Links, bonds, and noetherian bimodes; 6. The second layer; 7. Classical localization; 8. The second layer condition; 9. Indecomposable injectives and the second layer condition.