On the Associated Graded ring of Semigroup Algebras
Commutative Algebra
2022-10-17 v1
Abstract
In this paper, we give the necessary and sufficient conditions for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroups using Gr\"{o}bner basis. We generalize the concept of homogeneous numerical semigroup for the simplicial affine semigroup and show that the Betti numbers of the corresponding semigroup ring matches with the Betti numbers of the associated graded ring. We also define the nice extension for simplicial affine semigroups, motivated by the notion of a nice extension of the numerical semigroups.
Keywords
Cite
@article{arxiv.2210.07520,
title = {On the Associated Graded ring of Semigroup Algebras},
author = {Joydip Saha and Indranath Sengupta and Pranjal Srivastava},
journal= {arXiv preprint arXiv:2210.07520},
year = {2022}
}