Graded almost valuation ring
REVISTA DE LA UNION MATEMATICA ARGENTINA, cilt.2, ss.1-16, 2025 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2
- Basım Tarihi: 2025
- Dergi Adı: REVISTA DE LA UNION MATEMATICA ARGENTINA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Directory of Open Access Journals, DIALNET
- Sayfa Sayıları: ss.1-16
- Marmara Üniversitesi Adresli: Evet
Özet
Let R = α∈ΓRα beacommutative ring graded by an arbitrary torsionless monoid Γ. We say that R is graded almost valuation ring (gr AVring) if for every two homogeneous elements a,b of R, there exists a positive integer n such that either an divides bn (in R) or bn divides an. In this paper, we introduce and study the graded version of the almost valuation ring which is a generalization of gr-AVD to the context of arbitrary Γ-graded ring ( with zero-divisors). Next, we study the possible transfer of these property to the graded trivial ring extension (A ⋉E). Our aim is to provide examples of new classes of Γ-graded rings satisfying the above mentioned property.