Commutative graded-n-coherent and graded valuation rings - TEKİR, ÜNSAL (My University, 2022)
Let R = ⊕α∈GRα 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: Matematik; Değişmeli Halkalar ve Cebirler; Temel Bilimler; Mathematics; Commutative Rings and Algebras; Natural Sciences; Temel Bilimler (SCI); Doğa Bilimleri Genel; ÇOK DİSİPLİNLİ BİLİMLER; MATEMATİK; Natural Sciences (SCI); NATURAL SCIENCES, GENERAL; MATHEMATICS; MULTIDISCIPLINARY SCIENCES; Multidisciplinary; Discrete Mathematics and Combinatorics; Geometry and Topology; Logic; Physical Sciences; 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