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arXiv · 1208.5625

The index of a numerical semigroup ring

Oana Veliche
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Abstract

Let $R=k[|t^a,t^b,t^c|]$ be a complete intersection numerical semigroup ring over an infinite field $k$, where $a,b,c\in\BN$. The generalized Loewy length, which is Auslander's index in this case, is computed in terms of the minimal generators of the semigroup: $a,b$ and $c$. Examples provided show that the left hand side of Ding's inequality $\mult(R)-\inde(R)-\codim(R)+1\geq 0$ can be made arbitrarily large for rings $R$ with $\edim(R)=3$ . The index of a complete intersection numerical semigroup ring with embedding dimension greater than three is also computed.

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Oana Veliche. 2012-08-28. The index of a numerical semigroup ring. https://arxiv.org/abs/1208.5625

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