English

On the associated graded ring of a semigroup ring

Commutative Algebra 2015-03-17 v2

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.

Keywords

Cite

@article{arxiv.1004.5481,
  title  = {On the associated graded ring of a semigroup ring},
  author = {Marco D'Anna and Vincenzo Micale and Alessio Sammartano},
  journal= {arXiv preprint arXiv:1004.5481},
  year   = {2015}
}

Comments

20 pages

R2 v1 2026-06-21T15:16:53.317Z