The 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∈[s] of S such that each P _i is not contained in the sum of the other (P _j ) _j≠i .

Key Words:

• Monomial ideals
• Stanley decompositions
• Stanley depth

2010 Mathematics Subject Classification:

• Primary: 13C15
• Secondary: 13F20, 13F55, 13P10

ACKNOWLEDGMENTS

The support from the CNCSIS grant PN II-542/2009 of Romanian Ministry of Education, Research, and Inovation is gratefully acknowledged.

Notes

Communicated by U. Walther.