JP Journal of Algebra, Number Theory and Applications
Volume 19, Issue 2, Pages 185 - 201
(December 2010)
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ANOTHER GENERALIZED SAMUEL NUMBER
ON A SEMI-RING
Soma Ouattara, Eric Dago Akeke and Philippe Ayegnon
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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 and
then we have
Let f,
g and h
be filtrations on the semi-ring A.
Then we obtain