Singular and nonsingular modules relative to a torsion theory

Ceken S., ALKAN M.

COMMUNICATIONS IN ALGEBRA, vol.45, no.8, pp.3377-3389, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.1080/00927872.2016.1236930
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3377-3389
  • Keywords: tau-Essential submodule, tau-semisimple module, tau-singular module, non-tau-singular module
  • Akdeniz University Affiliated: Yes

Abstract

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.