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arXiv · 1804.10330

A short proof of Bresinski's Theorem on Gorenstein semigroup rings generated by 4 elements

Kei-ichi Watanabe
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Abstract

Let $H=\langle n_1, \ldots ,n_4\rangle$ be a numerical semigroup generated by $4$ elements, which is symmetric and let $k[H]$ be the semigroup ring of $H$ over a field $k$. H. Bresinski proved that the defining ideal of $k[H]$ is minimally generated by $3$ or $5$ elements. We give a new short proof of Bresinski's Theorem using the structure theorem of Buchsbaum and Eisenbud on the minimal free resolution of Gorenstein rings of embedding codimension $3$.

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Kei-ichi Watanabe. 2018-04-27. A short proof of Bresinski's Theorem on Gorenstein semigroup rings generated by 4 elements. https://arxiv.org/abs/1804.10330

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