Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 1, pp. 125-148, 2022

$n$-gr-coherent rings and Gorenstein graded modules

Mostafa Amini, Driss Bennis, Soumia Mamdouhi

Received August 17, 2020. Published online November 2, 2021.

Abstract: Let $R$ be a graded ring and $n\geq1$ 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.

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

Classification MSC: 16E30, 16D40,16D50, 16W50

DOI: 10.21136/CMJ.2021.0359-20

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Mostafa Amini (corresponding author), Department of Mathematics, Faculty of Sciences, Payame Noor University, Nakhl St, Lashkarak Highway, Tehran, Iran, e-mail: amini.pnu1356@gmail.com; Driss Bennis, Soumia Mamdouhi, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, B.P. 8007 Nations-Unies, Avenue des Nations Unies, Agdal, Rabat, Morocco, e-mail: driss.bennis@um5.ac.ma, driss_bennis@hotmail.com, soumiamamdouhi@yahoo.fr

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