Rings Characterized by Direct Sums of CS Modules
A Module M is called a CS module if every submodule of M is essential in a direct summand of M. In this dissertation certain classes of rings characterized by direct sums of CS modules are considered. It is proved that for a ring R for which either soc(RR) or E(RR) is finitely generated, the following hold: (i) R is a right Artinian ring and all uniform right R-modules are ?-quasi-injective iff for every CS right R-module M, M(N) is CS, and; (ii) R is a right Artinian ring and all uniform right R-modules have composition length at most two iff the direct sum of any two CS right R-modules is again CS. Partial answers are obtained to a question of Huynh whether a semilocal ring or a ring with finite right uniform dimension that is right countably ?-CS is right ?-CS. The results obtained in this dissertation yield, in particular, new characterizations of QF-rings. These results extend previously known results due to several authors such as Clark, Dung, Gómez Pardo, Guil Asensio, Huynh, Jain, López-Permouth, Müller, Oshiro and others.
School Location:USA - Ohio
Source Type:Master's Thesis
Keywords:artinian ring cs module uniform countably sigma
Date of Publication:01/01/2003