Semiregular modules with respect to a fully invariant submodule

Creative Commons License

Alkan M., Özcan A. Ç.

COMMUNICATIONS IN ALGEBRA, cilt.32, sa.11, ss.4285-4301, 2004 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 11
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1081/agb-200034143
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.4285-4301
  • Anahtar Kelimeler: semiregular modules, CS modules, quasi-injective modules, ACS rings, QF rings, RINGS, SEMIPERFECT, PERFECT
  • Akdeniz Üniversitesi Adresli: Hayır

Özet

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.