Neat-flat Modules


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Buyukasik E., Durgun Y.

COMMUNICATIONS IN ALGEBRA, vol.44, no.1, pp.416-428, 2016 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1080/00927872.2014.982816
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.416-428
  • Keywords: Closed submodule, (Co)neat submodule, Extending module, Neat-flat module, QF-ring
  • Çukurova University Affiliated: No

Abstract

Let R be a ring. A right R- module M is said to be neat- flat if the kernel of any epimorphism Y -> M is neat in Y, i. e., the induced map Hom(S, Y) -> Hom(S, M) is surjective for any simple right R-module S. Neat-flat right R-modules are projective if and only if R is a right Sigma-CS ring. Every cyclic neat-flat right R-module is projective if and only if R is right CS and right C-ring. It is shown that, over a commutative Noetherian ring R, (1) every neat-flat module is flat if and only if every absolutely coneat module is injective if and only if R congruent to A x B, wherein A is a QF-ring and B is hereditary, and (2) every neat-flat module is absolutely coneat if and only if every absolutely coneat module is neat-flat if and only if R congruent to A x B, wherein A is a QF-ring and B is Artinian with J(2)(B) = 0.