Simple-Direct-Projective Modules

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

COMMUNICATIONS IN ALGEBRA, cilt.44, sa.12, ss.5163-5178, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 12
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/00927872.2016.1147574
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.5163-5178
  • Anahtar Kelimeler: Artinian serial rings, C3-modules, D3-modules, Simple-direct-injective, Simple- direct-projective modules, Uniserial rings, RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

In this paper, we introduce and study the dual notion of simple-direct-injective modules. Namely, a right R-module M is called simple-direct-projective if, whenever A and B are submodules of M with B simple and M/AB(circle plus)M, then A(circle plus)M. Several characterizations of simple-direct-projective modules are provided and used to describe some well-known classes of rings. For example, it is shown that a ring R is artinian and serial with J(2)(R)=0 if and only if every simple-direct-projective right R-module is quasi-projective if and only if every simple-direct-projective right R -module is a D3-module. It is also shown that a ring R is uniserial with J(2)(R)=0 if and only if every simple-direct-projective right R-module is a C3-module if and only if every simple-direct-injective right R -module is a D3-module.