Semiregular modules with respect to a fully invariant submodule

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ALKAN M., Ozcan A. Ç.

COMMUNICATIONS IN ALGEBRA, vol.32, no.11, pp.4285-4301, 2004 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 11
  • Publication Date: 2004
  • Doi Number: 10.1081/agb-200034143
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4285-4301
  • Hacettepe University Affiliated: Yes


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.