Vol. 81, No. 2, 1979

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ISSN: 0030-8730
Two theorems on the prime divisors of zeros in completions of local domains

Louis Jackson Ratliff, Jr.

Vol. 81 (1979), No. 2, 537–545
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
Authors
Louis Jackson Ratliff, Jr.