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arXiv · 1004.5481

On the associated graded ring of a semigroup ring

Marco D'Anna·Vincenzo Micale·Alessio Sammartano
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Abstract

Let (R;m) be a numerical semigroup ring. In this paper we study the properties of its associated graded ring G(m). In particular, we describe the H^0_M for G(m) (where M is the homogeneous maximal ideal of G(m)) and we characterize when G(m) is Buchsbaum. Furthermore, we find the length of H^0_M as a G(m)-module, when G(m) is Buchsbaum. In the 3-generated numerical semigroup case, we describe the H^0_M in term of the Apery set of the numerical semigroup associated to R. Finally, we improve two characterizations of the Cohen-Macaulayness and Gorensteinness of G(m) given in [2] and [3], respectively.

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Marco D'Anna, Vincenzo Micale, Alessio Sammartano. 2010-04-30. On the associated graded ring of a semigroup ring. https://doi.org/10.1216/jca-2011-3-2-147

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