On separability properties in direct products of semigroups

Gerard Aidan O'Reilly, Martyn Quick, Nik Ruskuc

Research output: Contribution to journalArticlepeer-review

2 Downloads (Pure)

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 languageEnglish
Pages (from-to)333-352
Number of pages21
JournalMonatshefte für Mathematik
Volume197
Issue number2
DOIs
Publication statusPublished - 27 May 2021

Keywords

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

Fingerprint

Dive into the research topics of 'On separability properties in direct products of semigroups'. Together they form a unique fingerprint.

Cite this