Residual finiteness and related properties in monounary algebras and their direct products

De Witt, Bill

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Date

24/04/2021

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Abstract

In this paper we discuss the relationship between direct products of monounary algebras and their components, with respect to the properties of residual finiteness, strong/weak subalgebra separability, and complete separability. For each of these properties P, we give a criterion CP such that a monounary algebra A has property P if and only if it satisfies CP. We also show that for a direct product A×B of monounary algebras, A×B has property P if and only if one of the following is true: either both A and B have property P, or at least one of A or B are backwards-bounded, a special property which dominates direct products and which guarantees all P hold.

Citation

De Witt , B 2021 , ' Residual finiteness and related properties in monounary algebras and their direct products ' , Algebra Universalis , vol. 82 , 32 . https://doi.org/10.1007/s00012-021-00727-4

Publication

Algebra Universalis

Status

Peer reviewed

DOI

https://doi.org/10.1007/s00012-021-00727-4

ISSN

0002-5240

Type

Journal article

Rights

Copyright © 2021 The Author(s). 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/.

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/23091