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.
