Annales Mathematiques Africaines


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Contenu > Anciens Numéros > Volume_3

Filtrations, Transcendence Degree and Analytic Spread



Dramane Bio SALIFOU

70, boul. Henri-Bourassa Ouest
Montréal, QC, H3L 1M7, CANADA



Mathematics Subject Classifications:(2010 MSC) 13A30, 13E05 .
Key words: nœtherian filtration, Rees ring of a filltration, transcendence degree, analytic spread.


Abstract:


Let be an integer which may be infinite. Let  be a nœtherian filtration of the commutative ring and
let   (resp. ) be the ordinary (resp. the extended) Rees ring of the filtration . For each ideal of containing we consider the transcendence degree of the -algebra over . The main purpose of this paper is to prove that the number is also an extension of the usual analytic spread of a nœtherian filtration.


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