Integrally closed ideals and asymptotic prime divisors

Louis Jackson Ratliff, Jr.

Vol. 91 (1980), No. 2, 445–456

DOI: 10.2140/pjm.1980.91.445

Abstract

The first theorem characterizes local (Noetherian) domains that have a height one maximal ideal in their integral closure as those local domains whose maximal ideal M is a prime divisor (= associated prime) of the integral closure I_a of all nonzero ideals I contained in large powers of M. The second theorem describes (modulo a mild assumption) all local domains R that have the following property: for each ideal I in R and for all large n, all the ideals Iⁿ and (Iⁿ)_a have the same prime divisors.

Mathematical Subject Classification 2000

Primary: 13A17, 13A17

Secondary: 13E05

Milestones

Received: 29 August 1979

Published: 1 December 1980