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Neat-flat modules

By Engin Büyükaşık and Yılmaz Durğun

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 (Formula presented.) -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 ≅ A × 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 ≅ A × B, wherein A is a QF-ring and B is Artinian with J 2(B) = 0.Scientific and Technical Research Council of Turke

Topics: (Co)neat submodule, Closed submodule, Extending module, Neat-flat module, QF-ring
Publisher: Taylor & Francis
Year: 2016
DOI identifier: 10.1080/00927872.2014.982816
OAI identifier: oai:openaccess.iyte.edu.tr:8080:11147/5937
Provided by: DSpace@IZTECH
Journal:

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