\(\gamma\)-[weakly] covered orthodox semigroups. (Q2569296)

An orthodox semigroup \(S\) is a \(\gamma\)-covered orthodox semigroup if the least inverse congruences of \(S\) are covering congruences. An orthodox semigroup is \(\gamma\)-covered if and only if its subband of idempotents is an \(N\)-covering band. Characterization theorems are given for the \(N\)-covering bands. Similar results are obtained for weaker versions of these notions.