Upper and Lower Bounds for the Stanley Depth of Certain Classes of Monomial Ideals and Their Residue Class Rings

Abstract

We give an upper bound for the Stanley depth of the edge ideal of a complete k-partite hypergraph and as an application we give an upper bound for the Stanley depth of a monomial ideal in a polynomial ring S. We also give a lower and an upper bound for the cyclic module S/I associated to the complete k-partite hypergraph.

Key Words:

• Monomial ideals
• Stanley decomposition
• Stanley depth

2000 Mathematics Subject Classification:

• Primary: 13C15
• Secondary: 13P10
• 13F20
• 05E45
• 05C65

ACKNOWLEDGMENTS

The authors would like to express their gratitude to ASSMS of GC University Lahore for creating a very appropriate atmosphere for research work. This research is partially supported by HEC Pakistan.

Notes

Communicated by R. Wiegand.