Abstract
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.
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Original Russian Text © T.V. Pervukhina, 2013, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Vol. 19, No. 4.
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Pervukhina, T.V. The structure of finite monoids satisfying the relation ℛ = ℋ. Proc. Steklov Inst. Math. 287 (Suppl 1), 134–144 (2014). https://doi.org/10.1134/S0081543814090132
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DOI: https://doi.org/10.1134/S0081543814090132