Binomial Canonical Decompositions of Binomial Ideals

Abstract

In this article, we prove that every binomial ideal in a polynomial ring over an algebraically closed field of characteristic zero admits a canonical primary decomposition into binomial ideals. Moreover, we prove that this special decomposition is obtained from a cellular decomposition which is also defined in a canonical way and does not depend on the field.

Key Words:

• Binomial ideal
• Cellular decomposition
• Index of nilpotency
• Polynomial ring
• Primary decomposition

2000 Mathematics Subject Classification:

• Primary 13F20
• Secondary 13P99

ACKNOWLEDGMENT

This research is partially supported by National Plan I +D +I (project MTM2007-64704), by Junta de Extremadura and FEDER funds

Notes

Communicated by I. Swanson.