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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: 13A30, 13E05 .
Key words: noetherian fltration, Rees ring of a fltration, transcendence degree.

Abstract:

Let be a nœtherian filtration of the commutative ring and let (resp. $\Re (A,\,f)=$ be the ordinary (resp. the extended) Rees ring of the filtration For each ideal of we consider the transcendence degree $\tau _{J}(f)$ = trdeg of the $\dfrac{A}{J}-$ algebra over $\dfrac{A}{J}.$
The main purpose of this paper is to compute the number $\tau _{P}( f )$ where 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.