Semigroups for which every right congruence of finite index is finitely generated

Craig Miller

doi:10.1007/s00605-020-01391-x

Semigroups for which every right congruence of finite index is finitely generated

Craig Miller

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We call a semigroup S f-noetherian if every right congruence of finite index on S is finitely generated. We prove that every finitely generated semigroup is f-noetherian, and investigate whether the properties of being f-noetherian and being finitely generated coincide for various semigroup classes.

Original language	English
Number of pages	24
Journal	Monatshefte für Mathematik
Volume	First Online
Early online date	18 Feb 2020
DOIs	https://doi.org/10.1007/s00605-020-01391-x
Publication status	E-pub ahead of print - 18 Feb 2020

Keywords

Semigroup
Right congruence
Finite generation

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10.1007/s00605-020-01391-xLicence: CC BY

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Copyright © The Author(s) 2020. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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Cite this

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abstract = "We call a semigroup S f-noetherian if every right congruence of finite index on S is finitely generated. We prove that every finitely generated semigroup is f-noetherian, and investigate whether the properties of being f-noetherian and being finitely generated coincide for various semigroup classes.",

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N2 - We call a semigroup S f-noetherian if every right congruence of finite index on S is finitely generated. We prove that every finitely generated semigroup is f-noetherian, and investigate whether the properties of being f-noetherian and being finitely generated coincide for various semigroup classes.

AB - We call a semigroup S f-noetherian if every right congruence of finite index on S is finitely generated. We prove that every finitely generated semigroup is f-noetherian, and investigate whether the properties of being f-noetherian and being finitely generated coincide for various semigroup classes.

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KW - Finite generation

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JO - Monatshefte für Mathematik

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Semigroups for which every right congruence of finite index is finitely generated

Abstract

Keywords

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