The core of monomial ideals

2023/03/18 by Fouli, Louiza, Montaño, Jonathan, Polini, Claudia +1
#05E40. Secondary: 14F18 #13B22 #13C40 #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13A30

paper · doi:10.48550/arxiv.2303.10486

Abstract

The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal I satisfying certain residual conditions, showing that \rm core(I) coincides with the largest monomial ideal contained in a general reduction of I. We prove that the class of lex-segment ideals satisfies these residual conditions and study the core of lex-segment ideals generated in one degree. For monomial ideals that do not necessarily satisfy the residual conditions and that are generated in one degree, we conjecture an explicit formula for the core, and make progress towards this conjecture.

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• The Core of 0-Dimensional Monomial Ideals
• Core and residual intersections of ideals
• The structure of the core of ideals
• A formula for the core of an ideal
• On the core of ideals