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Matrix, Polynomial, and Group Ring Extensions

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Extensions of Rings and Modules

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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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Authors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA

    Gary F. Birkenmeier

  2. Department of Mathematics, Busan National University, Busan, South Korea

    Jae Keol Park

  3. Department of Mathematics, The Ohio State University at Lima, Lima, OH, USA

    S. Tariq Rizvi

Authors
  1. Gary F. Birkenmeier
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  2. Jae Keol Park
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  3. S. Tariq Rizvi
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Birkenmeier, G.F., Park, J.K., Rizvi, S.T. (2013). Matrix, Polynomial, and Group Ring Extensions. In: Extensions of Rings and Modules. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92716-9_6

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