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OU- OSU Ring Theory Seminar

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A Generalization of (Dual) Rickart Modules, by Burcu Ungor (Ankara University, Ankara, Turkey, and Ohio University Center of Ring Theory and its Applications.

What
  • Seminar
When May 03, 2013
from 04:45 PM to 05:45 PM
Where MW 154 (OSU-Columbus.)
Contact Name
Contact Phone 740-593-1258
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Abstract: In this talk, we introduce a notion of (dual) π-Rickart modules as a generalization of the notion of (dual) Rickart modules which was introduced and studied by Lee-Rizvi-Roman, and we give some properties of (dual) π-Rickart modules. Let R be an arbitrary ring with identity and M a right R-module with S= EndR(M). The module M is called {\it (dual) π-Rickart} if for any fS, there exist e2=eS and a positive integer n such that Kerfn=eM (Imfn=eM).  We prove that (dual) Rickart and (dual) π-Rickart modules are the same for the modules whose endomorphism rings are reduced. The concepts of π-Rickart and dual π-Rickart modules extend the concepts of generalized right principally projective and π-regular rings to the module theory, respectively. We obtain some characterizations of generalized right principally projective rings and π-regular rings in terms of π-Rickart modules and dual π-Rickart modules. Also a characterization of an n×n matrix ring over R being π-regular is provided. We investigate relations between a (dual) π-Rickart module and its endomorphism ring.
(This is a joint work with S. Halicioglu and A. Harmanci.)

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