Vol. 91, No. 2, 1980

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Integrally closed ideals and asymptotic prime divisors

Louis Jackson Ratliff, Jr.

Vol. 91 (1980), No. 2, 445–456

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 Ia 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
Received: 29 August 1979
Published: 1 December 1980
Louis Jackson Ratliff, Jr.