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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 2

On MF-projective modules

Yusuf Alagöz
Pages
471–482
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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

Finally, we characterize the rings whose $MF$-projective modules are projective.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the left orthogonal class of max-flat modules which are the homological objects related to s-pure exact sequences of modules and module homomorphisms.
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Key Findings & Data:Namely, a right module $A$ is called MF-projective if ${Ext}^{1}_{R}(A,B)=0$ for any max-flat right $R$-module $B$, and $A$ is called strongly MF-projective if ${Ext}^{i}_{R}(A,B)=0$ for all max-flat right $R$-modules $B$ and all $i\geq 1$.
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Conclusion & Impact:Finally, we characterize the rings whose $MF$-projective modules are projective.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:(Max-)flat modules · MF-projective modules · Max-hereditary rings

Abstract

In this paper, we study the left orthogonal class of max-flat modules which are the homological objects related to s-pure exact sequences of modules and module homomorphisms. Namely, a right module $A$ is called MF-projective if ${Ext}^{1}_{R}(A,B)=0$ for any max-flat right $R$-module $B$, and $A$ is called strongly MF-projective if ${Ext}^{i}_{R}(A,B)=0$ for all max-flat right $R$-modules $B$ and all $i\geq 1$. Firstly, we give some properties of $MF$-projective modules and SMF-projective modules. Then we introduce and study MF-projective dimensions for modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed. We characterize some classes of rings such as perfect rings, $QF$ rings and max-hereditary rings by $(S)MF$-projective modules. We also study the rings whose right ideals are MF-projective. Finally, we characterize the rings whose $MF$-projective modules are projective.

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Cite This Article

Alagöz, Y. (2022). On MF-projective modules. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 2, 471–482. https://ajindex.com/articles/529530

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