JP Journal of Algebra, Number Theory and Applications
Volume 36, Issue 2, Pages 123 - 139
(April 2015) http://dx.doi.org/10.17654/JPANTAApr2015_123_139 |
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ANOTHER GENERALIZED SAMUEL NUMBER ON A SEMI-RING
Eric Dago Akeke, Soma Ouattara and Philippe Ayegnon
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Abstract: The asymptotic theory of ideals originated with the investigations in a Noetherian ring A of the Samuel number associated with each pair of non-nilpotent ideals having the same radical and the limit being reached from below and It is well known that for all filtrations and on a semi-ring A, the sequence is convergent in where is the filtration and Then the number has been introduced. By considering the filtration we give another extension of We show, in the case where f is an AP-filtration, that the sequence is convergent in Then we put We get the following result:
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Keywords and phrases: ring, semi-ring, filtration, pseudo-valuation |
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