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Keywords:
$n$-gr-coherent ring; Gorenstein $n$-FP-gr-injective module; Gorenstein $n$-gr-flat module; cover; (pre)envelope
$n$-gr-coherent ring; Gorenstein $n$-FP-gr-injective module; Gorenstein $n$-gr-flat module; cover; (pre)envelope
Summary:
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.
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