Exact pairs of homogeneous zero divisors
Andrew R. Kustin, Janet Striuli, and Adela Vraciu

TL;DR
This paper investigates the constraints on the Hilbert function of standard graded Artinian algebras imposed by the presence of exact pairs of homogeneous zero divisors, showing that compressed level algebras lack such divisors.
Contribution
It establishes new restrictions on Hilbert functions for algebras with exact zero divisor pairs and proves that compressed level algebras cannot have homogeneous zero divisors.
Findings
Constraints on Hilbert functions from zero divisor pairs
Compressed level algebras have no homogeneous zero divisors
Identification of algebraic conditions related to zero divisors
Abstract
Let S be a standard graded Artinian algebra over a field k. We identify constraints on the Hilbert function of S which are imposed by the hypothesis that S contains an exact pair of homogeneous zero divisors. As a consequence, we prove that if S is a compressed level algebra, then S does not contain any homogeneous zero divisors.
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