η-Simple semigroups without zero and η ∗-simple semigroups with a least non-zero idempotent
Roman S. Gigoń · Semigroup Forum · 2012
A semigroup S is called η-simple if S has no semilattice congruences except S×S. Tamura in (Semigroup Forum 24:77–82, 1982) studied η-simple semigroups with a unique idempotent. In the present paper we consider a more general situation, that is, we investigate η-simple semigroups (without zero) with a least idempotent. Moreover, we study η ∗-simple semigroups with zero which contain a least non-zero idempotent.