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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 2

On MF-projective modules

Yusuf Alagöz(SIIRT UNIVERSITY)0000-0002-2535-4679
Sayfa
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Yayın Tarihi
2021-04-11
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Finally, we characterize the rings whose $MF$-projective modules are projective.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:Finally, we characterize the rings whose $MF$-projective modules are projective.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:(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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Bu Makaleye Atıf Yap

Alagöz, Y. (2021). On MF-projective modules. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 2. https://doi.org/10.15672/hujms.731098

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