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arXiv · 1111.1294

When the associated graded ring of a semigroup ring is Complete Intersection

Marco D'Anna·Vincenzo Micale·Alessio Sammartano
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Abstract

Let (R, m) be the semigroup ring associated to a numerical semigroup S. In this paper we study the property of its associated graded ring G(m) to be Complete Intersection. In particular, we introduce and characterise beta-rectangular and gamma-rectangular Ap\'ery sets, which will be the fundamental concepts of the paper and will provide, respectively, a sufficient condition and a characterisation for G(m) to be Complete Intersection. Then we use these notions to give four equivalent conditions for G(m) in order to be Complete Intersection.

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Marco D'Anna, Vincenzo Micale, Alessio Sammartano. 2011-11-05. When the associated graded ring of a semigroup ring is Complete Intersection. https://doi.org/10.1016/j.jpaa.2012.09.024

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