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Commutative graded- $S$ -coherent rings

Anass Assarrar; Najib Mahdou; Ünsal Tekir; Suat Koç — 2023

Czechoslovak Mathematical Journal

Recently, motivated by Anderson, Dumitrescu’s $S$ -finiteness, D. Bennis, M. El Hajoui (2018) introduced the notion of $S$ -coherent rings, which is the $S$ -version of coherent rings. Let $R = ⨁_{α \in G} R_{α}$ be a commutative ring with unity graded by an arbitrary commutative monoid $G$ , and $S$ a multiplicatively closed subset of nonzero homogeneous elements of $R$ . We define $R$ to be graded- $S$ -coherent ring if every finitely generated homogeneous ideal of $R$ is $S$ -finitely presented. The purpose of this paper is to give the graded...

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Commutative graded- S -coherent rings

Commutative graded- $S$ -coherent rings