The smallest regular semigroups with all four skew pairs of idempotents

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2 Citations (Scopus)

Abstract

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
Volume69
Issue number2
DOIs
Publication statusPublished - Sept 2004

Keywords

  • Idempotents
  • Regular semigroup
  • Skew pairs

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