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Comptes Rendus Mathématique
Volume 340, n° 1
pages 5-7 (janvier 2005)
Doi : 10.1016/j.crma.2004.11.017
Received : 4 May 2004 ;  accepted : 5 November 2004
When is   Noetherian?
Quand   est-il noethérien ?
 

Sana Hizem , Ali Benhissi
Department of Mathematics, Faculty of Sciences, 5000 Monastir, Tunisia 

Abstract

Let   be an extension of commutative rings with identity, X an analytic indeterminate over B , and  , the subring of the formal power series ring  , consisting of the series with constant terms in A . In this Note we study when the ring R is Noetherian. We prove that R is Noetherian if and only if A is Noetherian and B is a finitely generated A -module. To cite this article: S. Hizem, A. Benhissi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.
Résumé

Soient   une extension dʼanneaux commutatifs unitaires, X une indeterminée sur B , et  , le sous-anneau de lʼanneau des séries formelles  , formé par les séries dont le terme constant est dans A . Nous donnons une condition nécessaire et suffisante pour que lʼanneau R soit noethérien. Nous démontrons que R est noethérien si et seulement si A est noethérien et B est un A module de type fini. Pour citer cet article : S. Hizem, A. Benhissi, C. R. Acad. Sci. Paris, Ser. I 340 (2005).

The full text of this article is available in PDF format.


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