In this mathematical investigation, we show that certain graded k-algebras contain zero divisors, implying unique properties for their structure.
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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Eddings et al. (2026) studied this question.
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