Abstract
In this note it is proved that if R R is an integral domain the set of valuation ideals of R R is closed under intersection if and only if the integral closure of R R is a valuation ring. Let S S be a domain which is integrally dependent on R R and contains the integral closure of R R . Then the set of valuation ideals of R R is the same as the set of ideals of R R which contract from ideals of S S if and only if the set of valuation ideals of R R is closed under intersection.
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