Abstract
The Asymptotic Theory of ideals originated with the investigation in noetherian ring A of the Samuel numbers ⊢I(J) and [wbar]I(J) associ-ated to each pair (I, J) of nonnilpotent ideals having the same radical where , the limit being reached from below and
. The number [wbar]I(J) is defined in a symetric situation. As an answer of a question raised by Samuel, Nagata has shown that the set of deviations
is bounded. Here we extend these numbers to pairs (f,g), where f = (I
n) and g= (J
n) are filtrations on A, as follows:
, where f(r) is filtration (Inr
)
. We prove in particular that if f and g are separated, nonnilpotent, strongly AP filtrations and such
then the deviation sequence
is bounded in R+. A similar study is done concerning the sequence
and bf
(g) = ∞ if the last set is empty.