Remarks on canonical quasi-ideals in semigroups
A canonical quasi-ideal in a semigroup is defined as a non-zero intersection of a 0-minimal right ideal and a 0-minimal left ideal. The paper extends results on 0-minimal quasi-ideals of semiprime semigroups to canonical quasi-ideals of arbitrary semigroups. (In a semiprime semigroup every 0-minimal quasi-ideal is canonical.) It is proved e.g. that a semigroup has a completely 0-simple ideal iff it has an idempotent canonical quasi-ideal, and then primitive regular semigroups are characterized by using idempotent canonical quasi-ideals.
scientific article; zbMATH DE number 4105243