Graded almost valuation ring

Guissi F. Z., Mahdou N., Tekir Ü., Koç S.

REVISTA DE LA UNION MATEMATICA ARGENTINA, cilt.2, ss.1-16, 2025 (SCI-Expanded)

  • 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.