Three theorems on imbedded prime divisors of principal ideals

Louis Jackson Ratliff, Jr.

Vol. 49 (1973), No. 1, 199–210

DOI: 10.2140/pjm.1973.49.199

Abstract

Let B be a finitely generated integral domain over a Noetherian domain A. The first theorem shows that there are only finitely many imbedded prime divisors of principal ideals in B if and only if this holds in A. The second theorem gives a necessary and sufficient condition in order that only finitely many height one prime ideals in A ramify in B, when A is locally factorial. The third theorem characterizes local domains which contain infinitely many imbedded prime divisors of principal ideals.

Mathematical Subject Classification 2000

Primary: 13G05

Milestones

Received: 5 July 1972

Published: 1 November 1973