Communications in Algebra· 2026Q2
The non-pure dual exchange property in low dimensions
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- Q2SCImago
- 2026year
Short summary
In two variables, all integrally closed monomial ideals satisfy the non-pure dual exchange property, and strongly stable ideals in three variables satisfy it if their Borel generators meet simple degree inequalities.
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Key points
- Every integrally closed monomial ideal in two variables satisfies the non-pure dual exchange property.
- Polymatroidal ideals in two variables are characterized as a consequence of the above finding.
- A criterion for strongly stable ideals in three variables to satisfy the property is provided.
- This criterion involves checking simple inequalities on the degrees of the Borel generators.
AI-generated from the title and abstract; the full text is not read.
Abstract
We investigate monomial ideals satisfying the non-pure dual exchange property, a notion introduced in connection with componentwise polymatroidal ideals. Our contributions are twofold. First, we show that in two variables, every integrally closed monomial ideal satisfies this property; as a consequence, we characterize polymatroidal ideals in two variables. Second, for strongly stable (Borel) ideals in three variables, we establish a practical criterion: it suffices to verify the defining condition only for the Borel generators, and this verification reduces to simple inequalities involving the degrees in the second and third variables.
The authors' abstract, as published at the source. Communications in Algebra, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics