November 1, 2019 at 10:15 pm

Ring Theory Seminar | Nonsingular and Cononsingular Properties via Endomorphism Ring of Modules, Nov. 8

Cosmin Roman, portrait

Dr. Cosmin Roman

The Ohio University-Ohio State University Ring Theory Seminar Series presents Dr. Cosmin Roman discussing “Nonsingular and Cononsingular Properties via Endomorphism Ring of Modules” (a joint work with F. A. Ebrahim and S. T. Rizvi) on Friday, Nov. 8, at 4:45 p.m. in Cockins Hall 240, OSU-Columbus.

Roman is Associate Professor of Mathematics at Ohio State University-Lima.

Abstract: An important result in Ring Theory, relating two important notions: extending rings and Baer rings, is the Chatters-Khuri theorem (1980) stating that “A ring is extending and nonsingular if and only if the ring is Baer and cononsingular”. The two auxiliary properties that are invoked are very useful, and warranted study in various other settings (nonsingular rings are a staple notion in many research papers). More recently, with the advent of Baer property of modules, and the extension of Chatters-Khuri result to a module-theoretic setting, both nonsingular and cononsingular properties have been re-defined for modules, via the endomorphism ring of said modules. The new properties are dubbed $\mathcal K$-nonsingular module and $\mathcal K$-cononsingular module.

While the former was present quite often in research papers in the context of Baer modules, Rickart modules, and their generalizations, the latter property has not yet been given the same treatment.  However, since the concept of $\mathcal K$-cononsingular module generalizes that of extending module, it is worth attempting to correct this oversight. In this presentation, we will study this class of modules, investigating basic properties and presenting related notions. Examples  illustrating  these notions and delimiting our results will also be provided.

Leave a Reply

Your email address will not be published. Required fields are marked *