November 1, 2015 at 9:00 pm

Ring Theory Seminar | On Piecewise Prime Modules, Nov. 13

The Ohio University-Ohio State University Ring Theory Seminar presents Gangyong Lee (Sungkyunkwan University, Suwon, South Korea) discussing “On piecewise prime modules” on Friday, Nov. 13, at 4:45 p.m. in Cockins Hall 240, OSU-Columbus.

ABSTRACT: The notion of piecewise prime rings was introduced by Birkenmeier-Heatherly-Kim-Park in 2000. A quasi-Baer ring is said to be piecewise prime (PWP) if its endomorphism ring has a complete set of triangulating idempotents. It is known that the piecewise prime rings have a general triangular matrix representation with prime rings on the diagonal. As one of general module theoretic settings of a prime ring, an endorprime module was introduced, in 2005, by Haghany and Vedadi. A right $R$-module $M$ is said to be endoprime if any nonzero fully invariant submodule of $M$ is faithful as a left module over $End_R(M)$

In this talk, we extend the notion of a PWP ring and introduce a PWP (piecewise prime) module. A quasi-Baer module is called PWP if its endomorphism ring is PWP. We provide several properties of PWP modules.

In particular, we prove that every direct sum of copies of a PWP module is always a PWP module. We obtain an structure theorem completely describing a PWP module. As an important application of PWP modules, we prove that every column finite matrix ring over a PWP ring is always PWP. In particular, we show that endoprime modules are building blocks of PWP modules. Several characterizations of endoprime modules are shown. This talk is based on a joint work with S. Tariq Rizvi.

Leave a Reply

Your email address will not be published.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