REGULAR ANALYTIC INDEPENDENCE AND EXTENSIONS OF ANALYTIC SPREAD

ABSTRACT

The notion of Analytic Spread can be extended to filtrations by which denotes the maximum number of elements of J to be independent of order k with respect to a filtration f . Other extensions that we give in this paper are denoted by and . We show that if f is an adic filtration and a local ring with infinite residue field, then and are equal; but if f is not adic may be different from the other extensions, even if f is noetherian and A a local ring with infinite residue field. We introduce a weak notion, called regular analytic independence to which corresponds an extension denoted by and we show that if is a noetherian filtration with rank m and is a maximal ideal containing with infinite, then for all we have:

We also prove that in the general case, if J is maximal or contains then

Acknowledgments