Annales Mathematiques Africaines


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Contenu > Anciens Numéros > Volume_2

Extension aux quasi-graduations sur un semi-anneau des nombres de Samuel de deux idéaux




Youssouf M. Diagana


Soma Ouattara


UFR-SFA, Laboratoire de Math. et Inform.
Université d'Abobo-Adjamé, Abidjan, Côte d'Ivoires



Mathematics Subject Classifications:(MSC2010) 13A15; 13A99.
Key words : Semi-anneaux, Quasi-graduations, Nombres de Samuel.

Abstract:


Let $B$ be a semi-ring and MATH be a family of sub-monoides of $B$.

$g$ is called a quasi-graduation of $B$ if $H_{0}=A$ is a sub-semi-ring of $B$, $H_{\infty }=(0)$ and MATH

We generalize the numbers of Samuel $v_{I}(J)$ and MATH by putting for each semi-ideal $J$ and for MATH and MATH two quasi-graduations of the semi-ring $B,$

MATH
when this limit exists in MATH

We establish the following results :

1) If $g\ $ is decreasing or $g$ verifies :

$\forall p>m\geq 0$ $\exists \lambda >0$ such that for $k\geq \lambda ,$ MATH

then MATH exists in MATH and one has

MATH

2) Suppose that $g$ is an AP -quasi-graduation.

If $g$ is decreasing or $g$ verifies :

$\forall p>m\geq 0$ $\exists \lambda >0$ such that for $k\geq \lambda , $ MATH and MATH then MATH exists in MATH and one has

MATH

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