Annales Mathematiques Africaines


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Contenu > Anciens Numéros > Volume_1

TRANSCENDENCE DEGREE OF REES RINGS OF
NŒTHERIAN FILTRATIONS AND THEIR QUOTIENTS



Dramane Bio SALIFOU
01 BP 3690 ABIDJAN 01 Côte d'Ivoire


Daouda SANGARE
22 BP 1709 ABIDJAN, 22 Côte d'Ivoire



Mathematics Subject Classifications: 13 A 30, 13 E 05 .
Key words: noetherian fltration, Rees ring of a fltration, transcendence degree.

Abstract:


Let MATH be a nœtherian filtration of the commutative ring $A$ and let MATH (resp.$\Re (A,\,f)=$MATH be the ordinary (resp. the extended) Rees ring of the filtration $f.$ For each ideal $J$ of $A$ we consider the transcendence degree $\tau _{J}(f)$ = trdegMATH of the $\dfrac{A}{J}-$algebra MATH over $\dfrac{A}{J}.$
The main purpose of this paper is to compute the number $\tau _{P}( f )$ where $P$ is a prime ideal which satisfies some conditions. We end by giving examples of values of $\tau _{P}(f)$ where these conditions are not all fulfilled.

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