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Matrix, Polynomial, and Group Ring Extensions

In: Extensions of Rings and Modules

Author

Listed:
  • Gary F. Birkenmeier

    (University of Louisiana at Lafayette, Department of Mathematics)

  • Jae Keol Park

    (Busan National University, Department of Mathematics)

  • S. Tariq Rizvi

    (The Ohio State University at Lima, Department of Mathematics)

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.

Suggested Citation

  • Gary F. Birkenmeier & Jae Keol Park & S. Tariq Rizvi, 2013. "Matrix, Polynomial, and Group Ring Extensions," Springer Books, in: Extensions of Rings and Modules, edition 127, chapter 0, pages 189-215, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-92716-9_6
    DOI: 10.1007/978-0-387-92716-9_6
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