Stanley conjecture on intersections of four monomial prime ideals

Abstract

We show that the Stanley's Conjecture holds for an intersection of four monomial prime ideals of a polynomial algebra $S$ over a field and for an arbitrary intersection of monomial prime ideals $(P_i{)}_{i\in [s]}$ of $S$ such that $P_i\not\subset {\Sigma }_{1=j\ne i}^s{P}_j$ for all $i\in [s]$.

accepted to Communications in Algebra

References in corpus (3)

• An inequality between depth and Stanley depth
• Special Stanley Decompositions
• Values and bounds of the Stanley depth

Cited by in corpus (8)

• Depth of some square free monomial ideals
• Depth and minimal number of generators of square free monomial ideals
• Values and bounds of the Stanley depth
• Stanley Conjecture on intersection of three monomial primary ideals
• Stanley depth of edge ideals
• Stanley depth and size of a monomial ideal
• Monomial ideals of minimal depth and trivial modifications
• Graph and depth of a monomial squarefree ideal