Two theorems on the prime divisors of zeros in completions of local domains

Louis Jackson Ratliff, Jr.

Vol. 81 (1979), No. 2, 537–545

DOI: 10.2140/pjm.1979.81.537

Abstract

The first theorem concerns the number of minimal prime ideals of a given depth (= dimension) in the completion of a finite integral extension domain of a semi-local domain. The second theorem characterizes local domains that have a depth one prime divisor of zero in their completion as those local domains whose maximal ideal M is a prime divisor ( = associated prime) of all nonzero ideals contained in large powers of M.

Mathematical Subject Classification 2000

Primary: 13G05

Secondary: 13C15, 13B20

Milestones

Received: 12 July 1978

Published: 1 April 1979