Extensions of Rings and Modules

種類:

電子ブック

責任表示:

by Gary F. Birkenmeier, Jae Keol Park, S Tariq Rizvi

出版情報:

New York, NY : Springer New York : Imprint: Springer, 2013

著者名:

• Birkenmeier, Gary F.
• Park, Jae Keol
• Rizvi, S Tariq
• SpringerLink (Online service)

ISBN:

9780387927169 [0387927166]    

注記:

The focus of this monograph is the study of rings and modules which have a rich supply of direct summands with respect to various extensions. The first four chapters of the book discuss rings and modules which generalize injectivity (e.g., extending modules), or for which certain annihilators become direct summands (e.g., Baer rings). Ring extensions such as matrix, polynomial, group ring, and essential extensions of rings from the aforementioned classes are considered in the next three chapters. A theory of ring and module hulls relative to a specific class of rings or modules is introduced and developed in the following two chapters. While applications of the results presented can be found throughout the book, the final chapter mainly consists of applications to algebra and functional analysis. These include obtaining characterizations of rings of quotients as direct products of prime rings and descriptions of certain C*-algebras via (quasi-)Baer rings. Extensions of Rings and Modules introduces for the fir

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