no. 21-22
Algebra
The D+E[Γ⁎] construction from Prüfer domains and GCD-domains
[Construction D+E[Γ⁎] dʼanneaux de Prüfer et à pgcd]
Présenté par : Jean-Pierre Demailly
Lim, Jung Wook1 
1 Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1135-1138

Let D⊊E denote an extension of integral domains, Γ be a nonzero torsion-free grading monoid with Γ∩−Γ={0}, Γ⁎=Γ∖{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.

Soit D⊊E une extension dʼanneaux commutatifs intègres, Γ un monoïde commutatif simplifiable sans torsion non trivial tel que Γ∩−Γ={0}. On note Γ⁎=Γ∖{0} et soit D+E[Γ⁎]={f∈E[Γ]|f(0)∈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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.10.023

Lim, Jung Wook 1

1 Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea 
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Lim, Jung Wook. The $ D+E[{\Gamma }^{⁎}]$ construction from Prüfer domains and GCD-domains. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1135-1138. doi: 10.1016/j.crma.2011.10.023

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