By Gary F. Birkenmeier
The concentration of this monograph is the examine of earrings and modules that have a wealthy offer of direct summands with appreciate to numerous extensions. the 1st 4 chapters of the e-book speak about jewelry and modules which generalize injectivity (e.g., extending modules), or for which definite annihilators turn into direct summands (e.g., Baer rings). Ring extensions equivalent to matrix, polynomial, team ring, and crucial extensions of earrings from the aforementioned sessions are thought of within the subsequent 3 chapters. A concept of ring and module hulls relative to a selected type of jewelry or modules is brought and built within the following chapters. whereas functions of the implications offered are available in the course of the ebook, the ultimate bankruptcy commonly includes functions to algebra and sensible research. those contain acquiring characterizations of jewelry of quotients as direct items of major earrings and outlines of convinced C*-algebras through (quasi-)Baer jewelry.
Extensions of earrings and Modules introduces for the 1st time in publication form:
* Baer, quasi-Baer, and Rickart modules
* the idea of generalized triangular matrix earrings through units of triangulating idempotents
* A dialogue of crucial overrings that aren't jewelry of quotients of a base ring and Osofsky's examine at the self-injectivity of the injective hull of a ring
* purposes of the speculation of quasi-Baer earrings to C*-algebras
Each portion of the e-book is enriched with examples and routines which make this monograph beneficial not just for specialists but additionally as a textual content for complex graduate classes. historic notes look on the finish of every bankruptcy, and a listing of Open difficulties and Questions is supplied to stimulate additional learn during this zone.
With over four hundred references, Extensions of earrings and Modules may be of curiosity to researchers in algebra and research and to complex graduate scholars in mathematics.