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arXiv · 2206.03533

$w$-$\rm FP$-projective modules and dimension

Refat Abdelmawla Khaled Assaad·El Mehdi Bouba·Mohammed Tamekkante
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Abstract

Let $R$ be a ring. An $R$-module $M$ is said to be an absolutely $w$-pure module if and only if $\Ext^1_R(F,M)$ is a GV-torsion module for any finitely presented module $F$. In this paper, we introduce and study the concept of $w$-FP-projective module which is in some way a generalization of the notion of $\rm FP$-projective module. An $R$-module $M$ is said to be $w$-$\rm FP$-projective if $\Ext^1_R(M,N)=0$ for any absolutely $w$-pure module $N$. This new class of modules will be used to characterize (Noetherian) $DW$ rings. Hence, we introduce the $w$-$\rm FP$-projective dimensions of modules and rings. The relations between the introduced dimensions and other (classical) homological dimensions are discussed. Illustrative examples are given.

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Refat Abdelmawla Khaled Assaad, El Mehdi Bouba, Mohammed Tamekkante. 2022-06-07. $w$-$\rm FP$-projective modules and dimension. https://arxiv.org/abs/2206.03533

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