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2013 | OriginalPaper | Chapter

6. Matrix, Polynomial, and Group Ring Extensions

Authors : Gary F. Birkenmeier, Jae Keol Park, S. Tariq Rizvi

Published in: Extensions of Rings and Modules

Publisher: Springer New York

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Abstract

Transference of the ring properties discussed in previous chapters to various ring extensions is the focus of this chapter. Results developed earlier are utilized to do so. It is observed that the Baer property of a ring does not transfer to its ring extensions so readily and that this happens only under special conditions. However, it will be shown that the quasi-Baer property transfers to various matrix and polynomial ring extensions without any additional assumptions. An exploration of the transference of the two aforementioned properties as well as of the Rickart, extending, p.q.-Baer, and the FI-extending properties to various ring extensions of the given ring is carried out. The extensions of a ring considered, include its matrix (both finite and infinite), polynomial, Ore, and group ring extensions. A characterization of a semiprime quasi-Baer group algebra is presented as a consequence.

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previous chapter Triangular Matrix Representations and Triangular Matrix Extensions

next chapter Essential Overring Extensions-Beyond the Maximal Ring of Quotients

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Title: Matrix, Polynomial, and Group Ring Extensions
Authors: Gary F. Birkenmeier
Jae Keol Park
S. Tariq Rizvi
Publisher: Springer New York
Book: Extensions of Rings and Modules
Print ISBN: 978-0-387-92715-2

Electronic ISBN: 978-0-387-92716-9

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-0-387-92716-9_6

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