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

Authors : Anass ASSARRAR, Najib MAHDOU, Ünsal TEKİR, Suat KOÇ

Pages : 1047-1057

Doi:10.15672/hujms.947574

View : 32 | Download : 10

Publication Date : 2022-08-01

Article Type : Research Paper

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