Geodesic
$n$-${\rm gr}$-coherent rings and Gorenstein graded modules
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 125-148
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Let $R$ be a graded ring and $n\geq 1$ be an integer. We introduce and study the notions of Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules by using the notion of special finitely presented graded modules. On $n$-gr-coherent rings, we investigate the relationships between Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules. Among other results, we prove that any graded module in $R$-gr (or gr-$R$) admits a Gorenstein $n$-FP-gr-injective (or Gorenstein $n$-gr-flat) cover and preenvelope, respectively.
Let $R$ be a graded ring and $n\geq 1$ be an integer. We introduce and study the notions of Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules by using the notion of special finitely presented graded modules. On $n$-gr-coherent rings, we investigate the relationships between Gorenstein $n$-FP-gr-injective and Gorenstein $n$-gr-flat modules. Among other results, we prove that any graded module in $R$-gr (or gr-$R$) admits a Gorenstein $n$-FP-gr-injective (or Gorenstein $n$-gr-flat) cover and preenvelope, respectively.
DOI : 10.21136/CMJ.2021.0359-20
Classification : 16D40, 16D50, 16E30, 16W50
Keywords: $n$-gr-coherent ring; Gorenstein $n$-FP-gr-injective module; Gorenstein $n$-gr-flat module; cover; (pre)envelope 
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     title = {$n$-${\rm gr}$-coherent rings and {Gorenstein} graded modules},
     journal = {Czechoslovak Mathematical Journal},
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Amini, Mostafa; Bennis, Driss; Mamdouhi, Soumia. $n$-${\rm gr}$-coherent rings and Gorenstein graded modules. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 125-148. doi: 10.21136/CMJ.2021.0359-20

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