A characterisation of semigroups with only countably many subdirect products with Z

Ashley Michael William Clayton, Catherine Reilly, Nik Ruskuc*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let Z be the additive (semi)group of integers. We prove that for a finite semigroup S the direct product Z × S contains only countably many subdirect products (up to isomorphism) if and only if S is regular. As a corollary we show that Z × S has only countably many subsemigroups (up to isomorphism) if and only if S is completely regular.
Original languageEnglish
Number of pages10
JournalBulletin of the Australian Mathematical Society
VolumeFirst View
Early online date4 Oct 2024
DOIs
Publication statusE-pub ahead of print - 4 Oct 2024

Keywords

  • Direct product
  • Subdirect product
  • Subsemigroup
  • Regular semigroup
  • Completely regular semigroup

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