JP Journal of Algebra, Number Theory and Applications
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Abstract: The Asymptotic Theory of ideals originated with the
investigations in a Notherian ring A
of the Samuel number associated with each pair of nonnilpotent ideals having the
same radical and the limit being reached from below
and Here we extend this number to
filtrations and on a semi-ring A.
We show that the sequence is convergent in where is the filtration and Then the number has been introduced. We give another
extension of We show that the sequence is convergent in where is the filtration Then we put If I
and J are semi-ideals of the semi-ring A andthen we have Let f,
g and h
be filtrations on the semi-ring A.
Then we obtain
Keywords and phrases: ring, semi-ring, filtration, pseudo-valuation.
