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Largeur analytique d’une bifiltration d’anneau

Bocar Ibrahima TOURE (*), Boubacar HAMA (**) et Monzon TRAORE (***)
Département d’Enseignement et de Recherche en Mathématiques et d’Informatique,
Faculté des Sciences et Techniques (FST), Université des Sciences, des Techniques et
des Technologies de Bamako (USTTB) Bamako, MALI

Mathematics Subject Classification: (2010) 13A02, 13A30, 16W50, 16W70
Key words: filtrations, bifiltrations, bigraduations, fonctions de type polynomial, largeur analytique


In the present paper, we investigate the asymptotic behaviour of the numerical function φF : (m,n)↦-→dimk(       )
where F = (Im,n) is an (I,J)- good bifiltration on a nœtherian local ring (A,𝔐,k) and I and J are two ideals of A. Under these conditions the analytic spread of F is defined by λ𝔐(F) = 2 + degφF where degφF is the degree of φF if φF is non null.
In Theorems 1 and 2 of this article, we prove that

λ𝔐(F) = dim-R(A,F-)-
𝔐R (A,F ) = dim-----R-(A,-I,J)------
R(A,I,J) ∩𝔐R  (A, F) = dim-R-(A,I,J)-
𝔐R  (A,I,J),

where R(A,F) = (m,n)2Im,nXmY n and R(A,I,J) = (m,n)2ImJnXmY n where X and where Y are two indeterminates.

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