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- W2144459194 abstract "Let D be an integral domain, Γ be a torsion-free grading monoid with quotient group G, and D[Γ] be the semigroup ring of Γ over D. We show that if G is of type (0, 0, 0,…), then D[Γ] is a weakly factorial domain if and only if D is a weakly factorial GCD-domain and Γ is a weakly factorial GCD-semigroup. Let ℝ be the field of real numbers and Γ be the additive semigroup of nonnegative rational numbers. We also show that Γ is a weakly factorial GCD-semigroup, but ℝ[Γ] is not a weakly factorial domain." @default.
- W2144459194 created "2016-06-24" @default.
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- W2144459194 date "2009-08-18" @default.
- W2144459194 modified "2023-09-26" @default.
- W2144459194 title "Semigroup Rings as Weakly Factorial Domains" @default.
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- W2144459194 doi "https://doi.org/10.1080/00927870802502746" @default.
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