Generalization of Semiperfect Rings
Asian Resonance (P: ISSN No. 0976-8602 RNI No.UPENG/2012/42622 VOL.-IV, ISSUE-II, April-2015 E: ISSN No. 2349-9443 ) Abstract D.S. Singh Assistant Professor, Deptt. of Pure & Applied Mathematics, Guru Ghasidas Vishwavidyalaya, Bilaspur (C.G.) Any right R-module M is called a CS-module if every submodule of M is essential in a direct summand of M. A ring is said to be CS-ring if R as right R-module is CS[9].In this paper we study semiperfect ring in which each simple right R-module is essential in a direct summand of R. We call such ring as a extending for simple R-module. Here we find that for such rings, every simple R-module is weakly-injective if and only R is weakly –injective if and only if R is self-injective if and only if R is weaklysemisimple. Examples are constructed for which simple R-module is essential in a direct summand. for full paper please visit below link : http://www.socialresearchfoundation.com/upoadreserchpapers/1/44/1506261114061std.s.singh....