On the associated graded ring of semigroup algebras

Authors

Joydip Saha, Indian Statistical Institute, Kolkata
Indranath Sengupta, Indian Institute of Technology Gandhinagar
Pranjal Srivastava, Indian Institute of Technology Gandhinagar

Article Type

Research Article

Publication Title

Communications in Algebra

Abstract

In this paper, we give a necessary and sufficient condition for the Cohen-Macaulayness of the associated graded ring of a simplicial affine semigroup using Gröbner 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 discuss nice extensions for simplicial affine semigroups, a concept which is motivated by nice extensions of numerical semigroups.

First Page

4259

Last Page

4270

DOI

https://10.1080/00927872.2023.2203773

Publication Date

1-1-2023

Comments

Open Access, Green

Recommended Citation

Saha, Joydip; Sengupta, Indranath; and Srivastava, Pranjal, "On the associated graded ring of semigroup algebras" (2023). Journal Articles. 3967.
https://digitalcommons.isical.ac.in/journal-articles/3967