Residuated completely simple semigroups

Thomas Scott Blyth, G.A. Pinto

Research output: Contribution to journalArticlepeer-review


We consider particular compatible orders on a given completely simple semigroup Sx=M((x);I,Λ;P) where (x) is an ordered cyclic group with x > 1 and P11=x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.

Original languageEnglish
Pages (from-to)181-194
Number of pages14
JournalAlgebra Colloquium
Issue number2
Publication statusPublished - Jun 2014


  • Lexicographic order
  • Bootlace order
  • Residuated
  • Completely simple semigroup


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