Vol. 94, No. 1, 1981

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A characterization of locally Macaulay completions

Craig Huneke

Vol. 94 (1981), No. 1, 131–138
Abstract

The purpose of this note is to prove the following theorem.

Theorem 1.1. Let (R,m) be a Noetherian local ring of dimension d 1 and depth d 1. By R denote the completion of R in the m-adic topology. Then the following are equivalent:

  1. R is equidimensional and satisfies Serre’s property Sd1
  2. Hmd1(R) has finite length
  3. There exists an N > 0 such that if x1,,xd is a sequence of elements R with ht(xi1,,xij) = j for all j-elements subsets of {1,,n}, 1 j n, and if mi N, 1 i d, then x1m1,,xdmd is an unconditioned d-sequence.

Mathematical Subject Classification 2000
Primary: 13H99
Milestones
Received: 18 October 1979
Published: 1 May 1981
Authors
Craig Huneke
Univ of Kansas
KS
United States