Vol. 45, No. 1, 1973

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Divisorial complete intersections

James Michael Hornell

Vol. 45 (1973), No. 1, 217–227

A complete intersection in a commutative ring R with identity is a regular element f of R such that g R and glf IR (the integral closure of R in its total quotient ring) imply that g∕f R. It assumed that R is nonimbedded and that IR is a noetherian R-module, and it is proven that the set of complete intersections in R is the set of regular elements of R not contained in any of a certain finite set of prime ideals of R, the nonnormal divisorial prime ideals of R together with the prime ideals which occur as an imbedded prime ideal of a proper principal ideal of R. This finite set of prime ideals contains the associated prime ideals of the conductor of IR in R, but it is shown that this is not always an equality.

Mathematical Subject Classification 2000
Primary: 13A15
Received: 11 November 1971
Published: 1 March 1973
James Michael Hornell