Neat-flat Modules


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Buyukasik E. , Durgun Y.

COMMUNICATIONS IN ALGEBRA, cilt.44, ss.416-428, 2016 (SCI İndekslerine Giren Dergi) identifier identifier identifier

  • Cilt numarası: 44 Konu: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/00927872.2014.982816
  • Dergi Adı: COMMUNICATIONS IN ALGEBRA
  • Sayfa Sayıları: ss.416-428

Özet

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.