Exact pairs of homogeneous zero divisors

2013/04/01 by Andrew R. Kustin, Kustin, Andrew R., Janet Striuli +3
Mathematics · #13A02 #13D02 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A02 #msc:13D02

paper · pdf · doi:10.48550/arxiv.1304.0411

arxiv created 2013/04/01 · arxiv updated 2013/04/02

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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