Semiperfect modules with respect to a preradical

Ozcan A., ALKAN M.

COMMUNICATIONS IN ALGEBRA, cilt.34, sa.3, ss.841-856, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34 Sayı: 3
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1080/00927870500441593
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.841-856
  • Anahtar Kelimeler: Harada and co-Harada module, Noetherian QF-module, projective module, projective cover, semiperfect module, semisimple module, SEMIREGULAR MODULES, PERFECT MODULES, RINGS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this article, we consider the module theoretic version of I-semiperfect rings R for an ideal I which are defined by Yousif and Zhou (2002). Let M be a left module over a ring R , N is an element of sigma[M], and tau(M) a preradical on sigma[M]. We call N tau(M)-semiperfect in sigma[M] if for any submodule K of N , there exists a decomposition K = A circle plus B such that A is a projective summand of N in sigma[M] and B <= tau(M) (N). We investigate conditions equivalent to being a tau(M)-semiperfect module, focusing on certain preradicals such as Z(M) , Soc , and delta(M) . Results are applied to characterize Noetherian QF-modules (with Rad (M) <= Soc(M)) and semisimple modules. Among others, we prove that if every R-module M is Soc-semiperfect, then R is a Harada and a co-Harada ring.