Maximal Congruences on Some Semigroups
Jintana Sanwong, Robert Patrick Sullivan · Algebra Colloquium · 2007
In 1976 Howie proved that a finite congruence-free semigroup is a simple group if it has at least three elements but no zero element. Infinite congruence-free semigroups are far more complicated to describe, but some have been constructed using semigroups of transformations (for example, by Howie in 1981 and by Marques in 1983). Here, for certain semigroups S of numbers and of transformations, we determine all congruences ρ on S such that S/ρ is congruence-free, that is, we describe all maximal congruences on such semigroups S.