The $ D+E[{\Gamma }^{⁎}]$ construction from Prüfer domains and GCD-domains

Jung Wook Lim

doi:10.1016/j.crma.2011.10.023

Algebra

The

D + E [Γ^{⁎}]

construction from Prüfer domains and GCD-domains

Presented by: Jean-Pierre Demailly

Jung Wook Lim ¹

¹ Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea

Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1135-1138.

Abstract
Résumé

Let $D ⊊ E$ denote an extension of integral domains, Γ be a nonzero torsion-free grading monoid with $Γ \cap - Γ = {0}$ , $Γ^{⁎} = Γ ∖ {0}$ and $D + E [Γ^{⁎}] = {f \in E [Γ] | f (0) \in D}$ . In this paper, we give a necessary and sufficient criteria for $D + E [Γ^{⁎}]$ to be a Prüfer domain or a GCD-domain.

Soit $D ⊊ E$ une extension dʼanneaux commutatifs intègres, Γ un monoïde commutatif simplifiable sans torsion non trivial tel que $Γ \cap - Γ = {0}$ . On note $Γ^{⁎} = Γ ∖ {0}$ et soit $D + E [Γ^{⁎}] = {f \in E [Γ] | f (0) \in D}$ . Dans cette note, on donne des conditions nécessaires et suffisantes pour que $D + E [Γ^{⁎}]$ soit un anneau de Prüfer ou un anneau à pgcd.

Received: 2011-08-12
Accepted: 2011-10-24
Published online: 2011-11-01

DOI: 10.1016/j.crma.2011.10.023

Author's affiliations:

Jung Wook Lim ¹

¹ Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea

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     author = {Jung Wook Lim},
     title = {The $ D+E[{\Gamma }^{{\textasteriskcentered}}]$ construction from {Pr\"ufer} domains and {GCD-domains}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1135--1138},
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     year = {2011},
     doi = {10.1016/j.crma.2011.10.023},
     language = {en},
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Jung Wook Lim. The $ D+E[{\Gamma }^{⁎}]$ construction from Prüfer domains and GCD-domains. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1135-1138. doi : 10.1016/j.crma.2011.10.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.023/

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