Matrix, Polynomial, and Group Ring Extensions

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

Chapter Chapter 6 in Extensions of Rings and Modules, 2013, pp 189-215 from Springer

Abstract: 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.

Keywords: u.p.-monoid; Monoid ring; Generalized countable join; Derivation; Ore extension; Quantum n-space; Polycyclic-by-finite group; Infinite dihedral group (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-92716-9_6

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DOI: 10.1007/978-0-387-92716-9_6

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