Vol. 49, No. 1, 1973

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Three theorems on imbedded prime divisors of principal ideals

Louis Jackson Ratliff, Jr.

Vol. 49 (1973), No. 1, 199–210

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
Received: 5 July 1972
Published: 1 November 1973
Louis Jackson Ratliff, Jr.