Semiregular modules with respect to a fully invariant submodule
COMMUNICATIONS IN ALGEBRA, vol.32, no.11, pp.4285-4301, 2004 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 32 Issue: 11
- Publication Date: 2004
- Doi Number: 10.1081/agb-200034143
- Journal Name: COMMUNICATIONS IN ALGEBRA
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.4285-4301
- Keywords: semiregular modules, CS modules, quasi-injective modules, ACS rings, QF rings, RINGS, SEMIPERFECT, PERFECT
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: No
Abstract
Let M be a left R-module and F a submodule of M for any ring R. We call M F-semiregular if for every x is an element of M, there exists a decomposition M = A circle plus B such that A is projective, A less than or equal to Rx and Rx boolean AND B less than or equal to F. This definition extends several notions in the literature. We investigate some equivalent conditions to F-semiregular modules and consider some certain fully invariant submodules such as Z(M), Soc(M), delta(M). We prove, among others, that if M is a finitely generated projective module, then M is quasi-injective if and only if M is Z(M)-semiregular and M circle plus M is CS. If M is projective Soc(M)-semiregular module, then M is semiregular. We also characterize QF-rings R with J(R)(2) = 0.