Simple-direct-modules

Ibrahim Y., Kosan M. T., Truong Cong Quynh T. C. Q., Yousif M.

COMMUNICATIONS IN ALGEBRA, cilt.45, sa.8, ss.3643-3652, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 8
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/00927872.2016.1243697
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3643-3652
  • Anahtar Kelimeler: Artinian serial rings and uniserial rings, C3-and D3-modules, CS and lifting modules, simple-direct-injective and simple-direct-projective modules, SSP and SIP modules, INJECTIVE-MODULES, RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with AB, and (BM)-M-circle plus, then A(circle plus)M. Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M/AB(circle plus)M and B simple, then A(circle plus)M. In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject. For example, we show that a ring R is uniserial (artinian serial) with J(2)(R)=0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module).