Contenu
Filtrations, analytic spread, and integral dependence
Dramane Bio SALIFOU
107 31 Ave NE, Calgary, Alberta, T2E 2E8, Canada
Mathematics Subject Classification: (2010) 13A30, 13E05
Key words: nœtherian filtration, Rees ring, dimension, integral dependence,
analytic spread.
Abstract:
Given a positive integer k which may be infinite, an ideal J of a
commutative ring A and a filtration f of A, the purpose of this note is firstly, to
prove that the (Krull) dimension of the generalized Rees quotient ring
, where ℜ(A,f) is the generalized Rees quotient ring of the filtration
f, and that is denoted by λJ(f,k), extends the usual Analytic Spread of a
nœtherian filtration f of a nœtherian ring A. Secondly, if g is another
filtration of the nœtherian ring A which is integral over f, then the equality
λJ(g,k) = λJ(f,k) holds.