Maximal Congruences on Some Semigroups

• 来源期刊: 代数集刊（英文版）
• 关键词: congruence-free semigroup transformation
• 年，卷（期）: 2007,（2）
• 页码范围: 255-263
• 页数: 9页
• 语种: 英文

摘要

In 1976 Howie proved that a finite congruence-free semigroup is a simple group if it has at least three elements but no zero elementInfinite 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, forcertain semigroups S of numbers and of transformations, we determine all congruences p on S such that S/p is congruence-free, that is, we describe all maximal congruences on such semigroups S.