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

Miller, Craig

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Date

18/02/2020

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.

Citation

Miller , C 2020 , ' Semigroups for which every right congruence of finite index is finitely generated ' , Monatshefte für Mathematik , vol. First Online . https://doi.org/10.1007/s00605-020-01391-x

Publication

Monatshefte für Mathematik

Status

Peer reviewed

DOI

https://doi.org/10.1007/s00605-020-01391-x

ISSN

0026-9255

Type

Journal article

Rights

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/.

Description

The author would like to thank his supervisor, Professor Nik Ruškuc, for his advice and guidance during the writing of this paper, and EPSRC for financial support.

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/19569