Extensions aux filtrations des nombres de samuel associ#xE9;s aux id#xE9;aux

摘要

We prove the existence of the generalized Samuel number wbarf(g) and the equalityfor any AP filtration f = (In) and any filtration g = (Jn) on a ring A. It is shown that wbarf(g) #x2265; #x22A2;f(g) for all AP filtrations f and g where f is separated and nonnilpotent. Two real numbers #x101;f(g) and #x180;f(g) are introduced. It is shown that #x101;f(g) = #x22A2;f(g) if #x22A2;f(g) exists (resp if wbarf(g)exists). Several properties of numbers #x101;f(g) and #x180;f(g) are given. It follows a generalization of (1, Theorem 5. 6) and a generalization of (6, Theorem 2) given by the formulawhere f, g, h are filtrations on a ring A.