The Core of 0-Dimensional Monomial Ideals

Details The Core of 0-Dimensional Monomial Ideals The Core of 0-Dimensional Monomial Ideals

2006-09-05

arxiv.org/abs/math/0609152v2

Mathematics

Commutative Algebra

22 pages; corrections made in revised file

Scientific paper

The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas.

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