The D+E[Γ*] construction from Prüfer domains and GCD-domains

Jung Wook Lim

doi:10.1016/j.crma.2011.10.023

The D+E[Γ^*] construction from Prüfer domains and GCD-domains

Jung Wook Lim

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Let D{subset of with not equal to}E denote an extension of integral domains, Γ be a nonzero torsion-free grading monoid with Γ∩-Γ={0}, Γ^*=Γ{set minus}{0} and D+E[Γ^*]={f∈E[Γ]|f(0)∈D}. In this paper, we give a necessary and sufficient criteria for D+E[Γ^*] to be a Prüfer domain or a GCD-domain.

Original language	English
Pages (from-to)	1135-1138
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	349
Issue number	21-22
DOIs	https://doi.org/10.1016/j.crma.2011.10.023
State	Published - Nov 2011

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10.1016/j.crma.2011.10.023

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abstract = "Let D\{subset of with not equal to\}E denote an extension of integral domains, Γ be a nonzero torsion-free grading monoid with Γ∩-Γ=\{0\}, Γ*=Γ\{set minus\}\{0\} and D+E[Γ*]=\{f∈E[Γ]|f(0)∈D\}. In this paper, we give a necessary and sufficient criteria for D+E[Γ*] to be a Pr{\"u}fer domain or a GCD-domain.",

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AB - Let D{subset of with not equal to}E denote an extension of integral domains, Γ be a nonzero torsion-free grading monoid with Γ∩-Γ={0}, Γ*=Γ{set minus}{0} and D+E[Γ*]={f∈E[Γ]|f(0)∈D}. In this paper, we give a necessary and sufficient criteria for D+E[Γ*] to be a Prüfer domain or a GCD-domain.

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The D+E[Γ^*] construction from Prüfer domains and GCD-domains

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