Partial ordering and congruences on LA-semigroups
A left almost semigroup (LA-semigroup, for short) is a groupoid satisfying the left invertive law \((ab)c=(cb)a\) and one of the equivalent weak associative laws \((ab)c=b(ca)\) or \((ab)c=b(ac)\). An LA-semigroup S is called inverse if for every \(a\in S\) there is \(a'\in S\) (an inverse of a) such that \((aa')a=a\) and \((a'a)a'=a'\). The present paper studies properties of compatible partial orderings and of congruences on inverse LA-semigroups. In particular, the greatest idempotent-separating congruence on an inverse LA-semigroup is described in detail.
scientific article; zbMATH DE number 4214263