Abstract
Let I 1,·, I g be proper ideals of a Noetherian ring R. Then it is shown that I 1·I g=I 1∩·∩I g=∩ {I j:(I 1·I j−1I j>+1 ·I g) n; j=1,·,g} for all n≥1 if and only if each P ∈ Ass( R/ I 1· I g ) contains exactly one of the ideals I j . As an application it is shown that if I 1,·, I g are generated by disjoint nonempty subsets of a permutable R-sequence, then I m 1 1·I m g g=I m 1 1∩·∩I m g g=∩ }I m j j (I 1·I j−1I j+1 ·I g) n; j=1,·, g} and Ass( R/ I m 1· I m g )=∪ g j =1 Ass ( R/ I j ) for all positive integers m 1, ·, m g , n. Then asymptotic and essential theory versions of these results are proved.
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