Commutative graded-$n$-coherent and graded valuation rings

Year 2022, Volume: 51 Issue: 4, 1047 - 1057, 01.08.2022

Anass Assarrar , Najib Mahdou , Ünsal Tekir , Suat Koç

https://doi.org/10.15672/hujms.947574

Cited By: 1

Abstract

Let $R= \oplus_{ \alpha \in G} R_{\alpha}$ be a commutative ring with unity graded by an arbitrary grading commutative monoid $G$. For each positive integer, the notions of a graded-n-coherent module and a graded-n-coherent ring are introduced. In this paper many results are generalized from $n$-coherent rings to graded-$n$-coherent rings. In the last section, we provide necessary and sufficient conditions for the graded trivial extension ring to be a graded-valuation ring.

Keywords

coherent rings and modules, n-coherent rings and modules, graded modules and rings, graded-coherent rings and modules, graded-valuation rings, graded trivial extension ring

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