On separability properties in direct products of semigroups

Gerard Aidan O'Reilly; Martyn Quick; Nik Ruskuc

doi:10.1007/s00605-021-01570-4

On separability properties in direct products of semigroups

Gerard Aidan O'Reilly, Martyn Quick, Nik Ruskuc

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

Abstract

We investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subsemigroup separability. For each of these properties we examine under which conditions the property is preserved under direct products. We also consider if any of the properties are inherited by the factors in a direct product. We give necessary and sufficient conditions for finite semigroups to preserve the properties of strong subsemigroup separability and monogenic subsemigroup separability in a direct product.

Original language	English
Pages (from-to)	333-352
Number of pages	21
Journal	Monatshefte für Mathematik
Volume	197
Issue number	2
DOIs	https://doi.org/10.1007/s00605-021-01570-4
Publication status	Published - 27 May 2021

Keywords

Separability
Residual properties
Subsemigroup separability
Residual finiteness
Complete separability
Semigroups
Direct products
Congruences
Finite index congruence

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Cite this

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AU - Quick, Martyn

AU - Ruskuc, Nik

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Y1 - 2021/5/27

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AB - We investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subsemigroup separability. For each of these properties we examine under which conditions the property is preserved under direct products. We also consider if any of the properties are inherited by the factors in a direct product. We give necessary and sufficient conditions for finite semigroups to preserve the properties of strong subsemigroup separability and monogenic subsemigroup separability in a direct product.

KW - Separability

KW - Residual properties

KW - Subsemigroup separability

KW - Residual finiteness

KW - Complete separability

KW - Semigroups

KW - Direct products

KW - Congruences

KW - Finite index congruence

U2 - 10.1007/s00605-021-01570-4

DO - 10.1007/s00605-021-01570-4

M3 - Article

SN - 0026-9255

VL - 197

SP - 333

EP - 352

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

IS - 2

ER -

On separability properties in direct products of semigroups

Abstract

Keywords

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