Category of $n$-FCP-gr-projective modules with respect to special copresented graded modules

Year 2022, Volume: 32 Issue: 32, 157 - 175, 16.07.2022

Mostafa Amını Driss Bennıs Soumia Mamdouhı

https://doi.org/10.24330/ieja.1077596

Cited By: 1

Abstract

Let $R$ be a ring graded by a group $G$ and $n\geq1$ an integer. We introduce the
notion of $n$-FCP-gr-projective $R$-modules and by using of
special finitely copresented graded modules, we investigate that (1) there exist some equivalent characterizations of $n$-FCP-gr-projective modules and graded right modules of $n$-FCP-gr-projective dimension
at most $k$ over $n$-gr-cocoherent rings, (2) $R$ is right $n$-gr-cocoherent if and only if for every short exact sequence $0 \rightarrow A\rightarrow B\rightarrow C\rightarrow 0$ of graded right $R$-modules, where $B$ and $C$ are $n$-FCP-gr-projective, it follows that $A$ is $n$-FCP-gr-projective if and only if ($gr$-$\mathcal{FCP}_{n}$, $gr$-$\mathcal{FCP}_{n}^{\bot}$) is a hereditary cotorsion theory, where $gr$-$\mathcal{FCP}_n$ denotes the class
of $n$-FCP-gr-projective right modules. Then we examine some of the conditions equivalent to that each right $R$-module is $n$-FCP-gr-projective.

Keywords

$n$-gr-Cocoherent ring, special gr-copresented module, $n$-FCP-gr-projective module

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