Stanley Conjecture on intersection of three monomial primary ideals

Abstract

We show that the Stanley's Conjecture holds for an intersection of three monomial primary ideals of a polynomial algebra S over a field.

Lexsegment ideals of Hilbert depth 1

“…a monomial ideal I such that this I is the intersection of four prime monomial ideals [Pop10, 4.2], or the intersection of three monomial primary ideals [Zar,2.2], or an almost complete intersection ideal [Cim11, 1.9], or a general monomial ideal if the Krull dimension of the ring n ≤ 5 [Pop09,2.11]. • Determine the Stanley depth of special modules, e.g, almost clean modules [HVZ09], graded maximal ideals [BHK + 10], monomial complete intersection ideals [She09], and some squarefree Veronese ideals [Cim09], [KSSY11] and [GLS].…”