C-PURE SUBMODULES AND C-FLAT MODULES

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Journal of Universal Mathematics
Volume:4 Issue:2
C-PURE SUBMODULES AND C-FLAT MODULES

C-PURE SUBMODULES AND C-FLAT MODULES

Pages : 222-229

View : 54 | Download : 11

Publication Date : 2021-07-31

Article Type : Research Paper

Abstract :Let R be a ring. A right R-module A is said to be C-flat if the kernel of any epimorphism B → A is C-pure in B, i.e. the induced map Hominsert ignore into journalissuearticles values(C,B); → Hominsert ignore into journalissuearticles values(C,A); is surjective for any cyclic right R-module C. Projective modules are C-flat and C-flat modules are weakly-flat and neat-flat. In this article, it is discussed the connections between C-flat, weakly-flat, neat-flat and singly flat modules. It is shown that C-flat modules coincide with singly-projective modules over arbitrary rings. Next, several characterizations of certain classes of rings and modules via C-purity are considered. We prove that, every C-flat module is injective if and only if R is a QF ring. Moreover, we show that R is a CF ring if and only if every FP-injective right R-module is C-flat.
Keywords : Singly projective modules, C pure submodules, CPS rings

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