Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras

Higashitani, Akihiro; Tani, Koichiro

Journal of Pure and Applied Algebra, 2025, 229(1), 107854

Number of Access:214（2025-10-21 20:34 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/100381

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Title
Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras
Creator
NRID
1000060723385 1000060723385
ORCID
0000-0002-3824-425X 0000-0002-3824-425X
researchmap permalink
7000011220 7000011220
Scopus Author ID
36105210100 36105210100
CreatorName
Higashitani, Akihiro
CreatorName
Tani, Koichiro
Subject
Finitely generated
Monoid algebra
SAGBI basis
Description
Higashitani A., Tani K. Non-finitely generated monoids corresponding to finitely generated homogeneous subalgebras. Journal of Pure and Applied Algebra 229, 107854 (2025); https://doi.org/10.1016/j.jpaa.2024.107854.
Abstract
The goal of this paper is to study the possible monoids appearing as the associated monoids of the initial algebra of a finitely generated homogeneous k-subalgebra of a polynomial ring k[x1,…,xn]. Clearly, any affine monoid can be realized since the initial algebra of the affine monoid k-algebra is itself. On the other hand, the initial algebra of a finitely generated homogeneous k-algebra is not necessarily finitely generated. In this paper, we provide a new family of non-finitely generated monoids which can be realized as the initial algebras of finitely generated homogeneous k-algebras. Moreover, we also provide an example of a non-finitely generated monoid which cannot be realized as the initial algebra of any finitely generated homogeneous k-algebra.
Publisher
Elsevier B.V.
Source Title
Journal of Pure and Applied Algebra
Volume (Issue)
229(1)
Page
107854
Date of Issued
2025-01-01
Language
English
Handle URL
https://hdl.handle.net/11094/100381
PISSN
00224049
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.1016/j.jpaa.2024.107854
Access Rights
open access
CopyRight
This article is licensed under a Creative Commons Attribution 4.0 International License.
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Version of Record
Category
学術雑誌論文 Journal Article