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.
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