Matrix Algebras over Strongly Non-Singular Rings
Metadata Field | Value | Language |
---|---|---|
dc.contributor.advisor | Albrecht, Ulrich F. | |
dc.contributor.author | McQuaig, Bradley | |
dc.date.accessioned | 2014-03-31T16:07:08Z | |
dc.date.available | 2014-03-31T16:07:08Z | |
dc.date.issued | 2014-03-31 | |
dc.identifier.uri | http://hdl.handle.net/10415/4010 | |
dc.description.abstract | We consider some existing results regarding rings for which the classes of torsion-free and non-singular right modules coincide. Here, a right R-module M is non-singular if xI is nonzero for every nonzero x in M and every essential right ideal I of R, and a right R-module M is torsion-free if Tor1(M,R/Rr)=0 for every r in R. In particular, we consider a ring R for which the classes of torsion-free and non-singular right S-modules coincide for every ring S Morita-equivalent to R. We make use of these results, as well as the existence of a Morita-equivalence between a ring R and the n × n matrix ring Matn(R) to characterize rings whose n × n matrix ring is a Baer-ring. A ring is Baer if every right (or left) annihilator is generated by an idempotent. Semi-hereditary, strongly non-singular, and Utumi rings will play an important role, and we explore these concepts and relevant results as well. | en_US |
dc.rights | EMBARGO_NOT_AUBURN | en_US |
dc.subject | Mathematics and Statistics | en_US |
dc.title | Matrix Algebras over Strongly Non-Singular Rings | en_US |
dc.type | thesis | en_US |
dc.embargo.length | NO_RESTRICTION | en_US |
dc.embargo.status | NOT_EMBARGOED | en_US |