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

Bill De Witt

doi:10.1007/s00012-021-00727-4

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

Bill De Witt

Pure Mathematics

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

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.

Original language	English
Article number	32
Number of pages	22
Journal	Algebra Universalis
Volume	82
DOIs	https://doi.org/10.1007/s00012-021-00727-4
Publication status	Published - 24 Apr 2021

Keywords

Monounary algebra
Residually finite
Direct product

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10.1007/s00012-021-00727-4Licence: CC BY

deWitt_2021_AU_Residual_CC
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/.
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Cite this

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N2 - 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.

AB - 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.

KW - Monounary algebra

KW - Residually finite

KW - Direct product

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JO - Algebra Universalis

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ER -

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

Abstract

Keywords

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