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arXiv · 2407.16000

Rings for which general linear forms are exact zero divisors

Ayden Eddings·Adela Vraciu
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Abstract

We investigate the standard graded $k$-algebras over a field $k$ of characteristic zero for which general linear forms are exact zero divisors. We formulate a conjecture regarding the Hilbert function of such rings. We prove our conjecture in the case when the ring is a quotient of a polynomial ring by a monomial idea, and also in the case when the ideal is generated in degree 2 and all but one of the generators are monomials.

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Ayden Eddings, Adela Vraciu. 2024-07-22. Rings for which general linear forms are exact zero divisors. https://doi.org/10.2140/involve.2026.19.107

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