An Upper Bound for the Regularity of Ideals of Borel Type

Abstract

We show that the regularity of monomial ideals of K[x ₁,…, x _n ] (K being a field), whose associated prime ideals are totally ordered by inclusion is upper bounded by a linear function in n.

Key Words:

• Borel ideals
• Regularity
• Stable ideals

2000 Mathematics Subject Classification:

• Primary 13P10
• Secondary 13C05, 13D02

ACKNOWLEDGMENTS

The authors are highly grateful to the School of Mathematical Sciences, GC University, Lahore, Pakistan in supporting and facilitating this research. Our thanks goes also to Prof. Dorin Popescu for his encouragement and valuable suggestions.

Notes

Communicated by I. Swanson.