- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 4
- Commutative graded-$n$-coherent and graded valuation rings
Commutative graded-$n$-coherent and graded valuation rings
Authors : Anass Assarrar, Najib Mahdou, Ünsal Tekir, Suat Koç
Pages : 1047-1057
Doi:10.15672/hujms.947574
View : 12 | Download : 5
Publication Date : 2022-08-01
Article Type : Research
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