Vol. 68, No. 1, 1977

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Unmixed 2-dimensional local domains

Stephen Joseph McAdam

Vol. 68 (1977), No. 1, 153–160
Abstract

Let b,c be a system of parameters in a 2-dimensional local (Noetherian) domain (R,M). For n 0, the chain (bn : 1) (bn : c) (bn : c2) becomes stable. Thus define a function S(b,c,) by letting S(b,c,n) be the least integer k 0 such that (bn : ck) = (bn : ck+1). Ratliff has shown that R is unmixed if and only if S(b,c,) is bounded. This paper shows that if R is unmixed then for any 0d M there is an integer d 0 such that for any system of parameters b,c and any i 0,S(b,c,b + i) = c.

Mathematical Subject Classification 2000
Primary: 13H99
Milestones
Received: 1 June 1976
Published: 1 January 1977
Authors
Stephen Joseph McAdam