Rickart modules relative to singular submodule and dual Goldie torsion theory

ÜNGÖR B., HALICIOĞLU S., Harmanci A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.15, sa.8, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 8
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1142/s0219498816501425
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Z(.)-inverse split module, Z*(.)-inverse split module, Rickart module, QF-ring, BAER MODULES, RINGS
  • Ankara Üniversitesi Adresli: Evet

Özet

Let R be an arbitrary ring with identity and M a right R-module with the ring S = End(R)(M) of endomorphisms of M. The notion of an F-inverse split module M, where F is a fully invariant submodule of M, is defined and studied by the present authors. This concept produces Rickart submodules of modules in the sense of Lee, Rizvi and Roman. In this paper, we consider the submodule F of M as Z(M) and Z*(M), and investigate some properties of Z(M)-inverse split modules and Z*(M)-inverse split modules M. Results are applied to characterize rings R for which every free (projective) right R-module M is F-inverse split for the preradicals such as Z(.) and Z*(.).