Characterization of the pseudovariety generated by finite monoids satisfying ℛ = ℋ

Abstract

We consider the pseudovariety generated by all finite monoids on which Green’s relations ℛ and ℋ coincide. It is shown that any finite monoid S belonging to this pseudovariety divides the monoid of all upper triangular row-monomial matrices over a finite group with zero adjoined. The proof is constructive; given a monoid S, the corresponding group and the order of matrices can be effectively found.