Abstract
The aim of this paper is to give some structure theorem of certain integrally closed ideals in Noetherian rings. Let A be a Noetherian ring and I an ideal of A. Then an element x of A is said to be integral over Z if x satisfies an equation x” + c, x”- ’ + . . . + c, = 0 in A with ci E I’. The integral closure I of Z is by definition the set of elements in A which are integral over Z and the ideal Z is called integrally closed if f= I. Let uA(Z) (resp. ht, I) denote the smallest number of elements in systems of generators for Z (resp. the height of I). Let Min, A/Z be the set of minimal prime divisors of I. In this paper we shall study the problem when the ideals Z of A such that uA(Z) = ht, Z are integrally closed and our result is stated as follows:
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