Rings for which general linear forms are exact zero divisors

Eddings, Ayden; Vraciu, Adela

doi:10.2140/involve.2026.19.107

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Rings for which general linear forms are exact zero divisors

Ayden Eddings and Adela Vraciu

Vol. 19 (2026), No. 1, 107–120

DOI: 10.2140/involve.2026.19.107

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 ideal, and also in the case when the ideal is generated in degree 2 and all but one of the generators are monomials.

Keywords

exact zero divisors, Hilbert function, weak Lefschetz property, monomial ideals

Mathematical Subject Classification

Primary: 13A02, 13C13

Milestones

Received: 24 April 2024

Revised: 3 August 2024

Accepted: 25 August 2024

Published: 25 January 2026

Communicated by Scott T. Chapman

Authors

Ayden Eddings
Department of Mathematics University of Nebraska-Lincoln Lincoln, NE United States

Adela Vraciu
Department of Mathematics University of South Carolina Columbia, SC United States

Vol. 19, No. 1, 2026