ABSOLUTELY s-PURE MODULES AND NEAT-FLAT MODULES

Creative Commons License

Buyukasik E., Durgun Y.

COMMUNICATIONS IN ALGEBRA, vol.43, no.2, pp.384-399, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1080/00927872.2013.842246
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.384-399
  • Keywords: Absolutely s-pure module, Injective cover, Kasch ring, Neat submodule, Simple-projective module, s-Pure submodule, RINGS, SUBMODULES, COVERS
  • Çukurova University Affiliated: No

Abstract

Let R be a ring with an identity element. We prove that R is right Kasch if and only if injective hull of every simple right R-modules is neat-flat if and only if every absolutely pure right R-module is neat-flat. A commutative ring R is hereditary and noetherian if and only if every absolutely s-pure R-module is injective and R is nonsingular. If every simple right R-module is finitely presented, then (1) R-R is absolutely s-pure if and only if R is right Kasch and (2) R is a right Sigma-CS ring if and only if every pure injective neat-flat right R-module is projective if and only if every absolutely s-pure left R-module is injective and R is right perfect. We also study enveloping and covering properties of absolutely s-pure and neat-flat modules. The rings over which every simple module has an injective cover are characterized.