LRT-biordered sets. (Q871622)

Call a regular semigroup \(S\) an RT-semigroup if \(S\) contains an idempotent subsemigroup \(I\) which is a left regular band and has non-empty intersection with every \(\mathcal R\)-class of \(S\); define an LT-semigroup dually, and let an LRT-semigroup one that is RT as well as LT. The class of semigroups so obtained forms a generalization of the class of all regular semigroups with an inverse transversal. Each semigroup obtained in this way admits an inverse unary operation \(a\mapsto a^\circ\) and the class of all unary semigroups obtained in this way forms a variety of regular unary semigroups. The main topic of the paper is to study the structure of the biordered set of idempotents of such semigroups.