学術雑誌論文

学術雑誌論文

text

Semigroup Forum. 2024, 108(1), p. 101-114

Difference of Hilbert series of homogeneous monoid algebras and their normalizations

Higashitani, Akihiro

Springer

英語

text

2024-03-11

https://doi.org/10.1007/s00233-024-10414-0

The version of record of this article, first published in Semigroup Forum, is available online at Publisher’s website: https://doi.org/10.1007/s00233-024-10414-0.

Let Q be an affine monoid, k[Q] the associated monoid k-algebra, and k[Q¯] its normalization, where we let k be a field. We discuss a difference of the Hilbert series of k[Q] and k[Q¯] in the case where k[Q] is homogeneous (i.e., standard graded). More precisely, we prove that if k[Q] satisfies Serre’s condition (S₂), then the degree of the h-polynomial of k[Q] is always greater than or equal to that of k[Q¯]. Moreover, we also show counterexamples of this statement if we drop the assumption (S₂).

This article is licensed under a Creative Commons Attribution 4.0 International License.

95020

Difference of Hilbert series of homogeneous monoid algebras and their normalizations

Higashitani, Akihiro

Springer

英語

2024-03-11

Semigroup Forum

108

1

101

114

https://doi.org/10.1007/s00233-024-10414-0

https://hdl.handle.net/11094/95020