Geodesic
Characterization of the pseudovariety generated by finite monoids satisfying $\mathscr{R}=\mathscr{H}$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 197-204 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the pseudovariety generated by all finite monoids on which Green's relations $\mathscr{R}$ and $\mathscr{H}$ 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.
Keywords: finite monoids; monoid pseudovariety; upper-triangular matrices; Green's relations; $\mathscr{R}$-trivial monoids. 
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T. V. Pervukhina. Characterization of the pseudovariety generated by finite monoids satisfying $\mathscr{R}=\mathscr{H}$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 197-204. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a19/

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