Residuated regular semigroups
T. S. Blyth, Gama Pinto · Proceedings of the Edinburgh Mathematical Society · 1992
We prove that in a residuated regular semigroup the elements of the form and are idempotents, and derive some consequences of this fact. In particular, we show how the maximality of such idempotents is related to the semigroup being naturally ordered, and obtain from this a characterisation of the boot-lace semigroup of [2].