The smallest regular semigroups with all four skew pairs of idempotents

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


An ordered pair (e, f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas f e is idempotent. We have shown previously that there are four distinct types of skew pairs of idempotents. Here we consider the smallest regular semigroups that contain precisely one of each of these four types. We show that, to within isomorphism and dual isomorphism, there are six such semigroups and characterise them as quotient semigroups of certain regular Rees matrix semigroups.

Original languageEnglish
Pages (from-to)230-242
Number of pages13
JournalSemigroup Forum
Issue number2
Publication statusPublished - Sept 2004


  • Idempotents
  • Regular semigroup
  • Skew pairs


Dive into the research topics of 'The smallest regular semigroups with all four skew pairs of idempotents'. Together they form a unique fingerprint.

Cite this