Regular orthocryptou semigroups. (Q706051)

The semigroups in this paper are defined using two kinds of generalized Green's relations defined elsewhere. A semigroup \(S\) is superabundant if each \(H^*\)-class contains an idempotent and \(S\) is semisuperabundant if both each \(\widetilde L\)- and \(\widetilde R\)-class contains at least one idempotent. A semigroup is a \(u\)-semigroup if it has just one idempotent that is its identity element. A semisuperabundant semigroup \(S\) is called an orthocryptou semigroup if \(\widetilde H\) on \(S\) is a congruence and \(E(S)\) is a subsemigroup of \(S\); the authors then say \(S\) is regular if \(E(S)\) forms a regular band. The main theorem is that a semigroup is a regular orthocryptou semigroup if and only if it is a so-called refined semilattice of rectangular \(u\)-semigroups.