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Journals / Journal of Universal Mathematics / 2021 / Cilt: 4 Sayı: 2

C-PURE SUBMODULES AND C-FLAT MODULES

Yusuf Alagöz(siirt üniversitesi)0000-0002-2535-4679
Pages
222–229
Publication Date
2021-07-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Moreover, we show that R is a CF ring if and only if every FP-injective right R-module is C-flat.

📌 3 Key Takeaways

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Objective & Hypothesis: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 Hom(C,B) → Hom(C,A) is surjective for any cyclic right R-module C.
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Key Findings & Data:Projective modules are C-flat and C-flat modules are weakly-flat and neat-flat.
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Conclusion & Impact:Moreover, we show that R is a CF ring if and only if every FP-injective right R-module is C-flat.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Singly projective modules · C-pure submodules · CPS rings

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 Hom(C,B) → Hom(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.

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Cite This Article

Alagöz, Y. (2021). C-PURE SUBMODULES AND C-FLAT MODULES. Journal of Universal Mathematics, Cilt: 4 Sayı: 2, 222–229. https://doi.org/10.33773/jum.952394

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