Special Stanley Decompositions

Abstract

Let $I$ be an intersection of three monomial prime ideals of a polynomial algebra $S$ over a field. We give a special Stanley decomposition of $I$ which provides a lower bound of the Stanley depth of $I$, greater than or equal to $\depth\ (I)$, that is, Stanley's Conjecture holds for $I$.

References in corpus (2)

• Stanley depth of complete intersection monomial ideals
• An inequality between depth and Stanley depth

Cited by in corpus (11)

• Stanley conjecture on intersections of four monomial prime ideals
• Depth of some square free monomial ideals
• Depth and minimal number of generators of square free monomial ideals
• Three generated, squarefree, monomial ideals
• Stanley Conjecture on intersection of three monomial primary ideals
• Depth in a pathological case
• Stanley depth and size of a monomial ideal
• Size and Stanley depth of monomial ideals
• Bounds on the Stanley depth and Stanley regularity of edge ideals of clutters
• Several inequalities regarding sdepth
• Graph and depth of a monomial squarefree ideal