Singular and nonsingular modules relative to a torsion theory

Ceken S., ALKAN M.

COMMUNICATIONS IN ALGEBRA, cilt.45, sa.8, ss.3377-3389, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 8
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1080/00927872.2016.1236930
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3377-3389
  • Anahtar Kelimeler: tau-Essential submodule, tau-semisimple module, tau-singular module, non-tau-singular module
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this paper, we introduce and study torsion-theoretic generalizations of singular and nonsingular modules by using the concept of -essential submodule for a hereditary torsion theory . We introduce two new module classes called -singular and non--singular modules. We investigate some properties of these module classes and present some examples to show that these new module classes are different from singular and nonsingular modules. We give a characterization of -semisimple rings via non--singular modules. We prove that if M/(M) is non--singular for a module M, then every submodule of M has a unique -closure. We give some properties of the torsion theory generated by the class of all -singular modules. We obtain a decomposition theorem for a strongly -extending module by using non--singular modules.