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Recenzirano
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Bakkari, Chahrazade; Mahdou, Najib; Riffi, Abdelkbir
Vietnam journal of mathematics, 12/2021, Letnik: 49, Številka: 4Journal Article
Let Γ be a torsionless grading monoid, R = ⊕ α ∈ Γ R α a Γ-graded integral domain, H the set of nonzero homogeneous elements of R , K the quotient field of R 0 and G 0 the group of units of Γ. We say that R is a graded almost valuation domain (gr-AVD) if for every nonzero homogeneous element x ∈ R H , there exists an integer n = n ( x ) ≥ 1 with x n or x − n ∈ R . In this paper, we show that R is a gr-AVD if and only if the following conditions hold. Γ is an almost valuation monoid, K ⊆ R H 0 is a root extension, If α ∈Γ is not a unit, then for every 0 ≠ x ∈ R α and 0 ≠ r ∈ R 0 , r n ∣ x n in R for some n ≥ 1, and T = ⊕ α ∈ G 0 R α is a gr-AVD.
