Locally quasi-unmixed Noetherian rings and ideals of the principal class

Louis Jackson Ratliff, Jr.

Vol. 52 (1974), No. 1, 185–205

DOI: 10.2140/pjm.1974.52.185

Abstract

It is proved that a Noetherian ring R is locally quasi-unmixed if and only if, for each ideal B of the principal class in R,(Bⁱ)_a is height unmixed, for all i > 0, where I_a denotes the integral closure in R of an ideal I in R. Three applications are given.

Mathematical Subject Classification 2000

Primary: 13H10

Milestones

Received: 19 September 1973

Published: 1 May 1974