Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/5937
Title: Neat-flat modules
Authors: Büyükaşık, Engin
Durğun, Yılmaz
Keywords: (Co)neat submodule
Closed submodule
Extending module
Neat-flat module
QF-ring
Publisher: Taylor and Francis Ltd.
Source: Büyükaşık, E., and Durğun, Y. (2016). Neat-flat modules. Communications in Algebra, 44(1), 416-428. doi:10.1080/00927872.2014.982816
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.
URI: http://doi.org/10.1080/00927872.2014.982816
http://hdl.handle.net/11147/5937
ISSN: 0092-7872
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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