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- W4221096243 abstract "Let $R$ be a ring graded by a group $G$ and $ngeq1$ 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 $0 rightarrow Arightarrow Brightarrow Crightarrow 0$ 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." @default.
- W4221096243 created "2022-04-03" @default.
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- W4221096243 date "2022-07-16" @default.
- W4221096243 modified "2023-10-18" @default.
- W4221096243 title "Category of $n$-FCP-gr-projective modules with respect to special copresented graded modules" @default.
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- W4221096243 doi "https://doi.org/10.24330/ieja.1077596" @default.
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