Eventually regular Dubreil-Jacotin semigroups

T S Blyth, G A Pinto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We derive necessary and sufficient conditions for an ordered eventually regular semigroup to be a Dubreil-Jacotin semigroup. We show that an eventually regular Dubreil-Jacotin semigroup has a biggest idempotent. Necessary and sufficient conditions for this biggest idempotent to be a weak middle unit or to be medial are related to the semigroup being naturally ordered and to the set of regular elements being a subsemigroup.

Original languageEnglish
Pages (from-to)431-440
Number of pages10
JournalSemigroup Forum
Volume69
DOIs
Publication statusPublished - Nov 2004

Keywords

  • eventually regular semigroup
  • Dubreil-Jacotin semigroup
  • weak middle unit
  • medial idempotent

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