STRONGLY NONCOSINGULAR MODULES

Alagoz Y., Durgun Y.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.42, no.4, pp.999-1013, 2016 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1182/blood-2016-07-726547
  • Journal Name: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.999-1013
  • Keywords: coclosed submodules, (non) cosingular modules, coatomic modules, ENDOMORPHISM-RINGS, CONEAT SUBMODULES
  • Çukurova University Affiliated: No

Abstract

An R-module M is called strongly noncosingular if it has no nonzero Rad-small (cosingular) homomorphic image in the sense of Harada. It is proven that (1) an R-module M is strongly noncosingular if and only if M is coatomic and noncosingular; (2) a right perfect ring R is Artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingular R-modules; (3) absolutely coneat modules are strongly noncosingular if and only if R is a right max ring and injective modules are strongly noncosingular; (4) a commutative ring R is semisimple if and only if the class of injective modules coincides with the class of strongly noncosingular R-modules.