2013
DOI: 10.1080/00927872.2012.699568
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The Stanley Conjecture on Intersections of Four Monomial Prime Ideals

Abstract: 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∈ [s] of S such that each P i is not contained in the sum of the other (P j ) j =i .

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Cited by 20 publications
(33 citation statements)
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“…Let Γ be the simple graph on [s] given by {ij} is an edge (we write {ij} ∈ E(Γ)) if and only if P i + P j = m. We call Γ the graph associated to I. Γ has the triangle property if there exists i ∈ [s] such that for all j, k ∈ [s] with {ij}, {ik} ∈ E(Γ) it follows that {jk} ∈ E(Γ). In fact the triangle property says that it is possible to find a "good" main prime in the terminology of [8…”
Section: Depth Two and Threementioning
confidence: 99%
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“…Let Γ be the simple graph on [s] given by {ij} is an edge (we write {ij} ∈ E(Γ)) if and only if P i + P j = m. We call Γ the graph associated to I. Γ has the triangle property if there exists i ∈ [s] such that for all j, k ∈ [s] with {ij}, {ik} ∈ E(Γ) it follows that {jk} ∈ E(Γ). In fact the triangle property says that it is possible to find a "good" main prime in the terminology of [8…”
Section: Depth Two and Threementioning
confidence: 99%
“…This conjecture holds for arbitrary monomial squarefree ideals if n ≤ 5 by [7] (see especially the arXiv version), or for intersections of four monomial prime ideals by [5], [8]. In the case of nonsquarefree monomial ideals J, an important inequality is sdepth J ≤ sdepth √ J (see [ The purpose of this paper is to study the case when bigsize(I) = 2, size(I) = 1.…”
Section: Introductionmentioning
confidence: 99%
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