Abstract
We characterize monomial ideals which are intersections of powers of monomial prime ideals and study classes of ideals with this property, among them polymatroidal ideals.
Highlights
In this paper we study monomial ideals which are intersections of powers of monomial prime ideals, and call them monomial ideals of intersection type
Any squarefree monomial ideal is of intersection type since it is an intersection of monomial prime ideals
We consider classes of ideals which are of intersection type. It is shown in Proposition 5 that any polymatroidal ideal is of strong intersection type, and in Theorem 8 we show that the canonical primary decomposition of polymatroidal ideals is given in terms of the rank function of the underlying polymatroid
Summary
In this paper we study monomial ideals which are intersections of powers of monomial prime ideals, and call them monomial ideals of intersection type. (a) The following conditions are equivalent: (i) I is an intersection of powers of monomial prime ideals; (ii) for all p ∈ Ass(S/I) there exist positive integers ap such that
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