The structure of finite monoids satisfying the relation ℛ = ℋ
T. V. Pervukhina · Proceedings of the Steklov Institute of Mathematics · 2014
It is shown that any finite monoid S on which Green’s relations R and H coincide divides the monoid of all upper triangular row-monomial matrices over a finite group. The proof is constructive; given the monoid S , the corresponding group and the order of matrices can be effectively found. The obtained result is used to identify the pseudovariety generated by all finite monoids satisfying R = H with the semidirect product of the pseudovariety of all finite groups and the pseudovariety of all finite R -trivial monoids.