Strongly E-reflexive inverse semigroups

Abstract

Let S be an inverse semigroup with semilattice of idempotents E. We denote by σ the minimum group congruence on S (6), and by τ the maximum idempotent-determined congruence on S (2). (Recall that the congruence η on S is called idempotent-determined if (e, x)∈ η and e ∈ E imply that x ∈ E.) In general τ ⊆ σ.