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.
Citation:
T. V. Pervukhina, “The structure of finite monoids satisfying the relation R=H”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 181–191; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 134–144
\Bibitem{Per13}
\by T.~V.~Pervukhina
\paper The structure of finite monoids satisfying the relation $\mathscr{R}=\mathscr{H}$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 4
\pages 181--191
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 287
\issue , suppl. 1
\pages 134--144
\crossref{https://doi.org/10.1134/S0081543814090132}
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Linking options:
https://www.mathnet.ru/eng/timm1012
https://www.mathnet.ru/eng/timm/v19/i4/p181
This publication is cited in the following 2 articles:
T. V. Pervukhina, “Characterization of the pseudovariety generated by finite monoids satisfying R=H”, Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 245–252
T. V. Pervukhina, “On the pseudovariety generated by all finite monoids satisfying R=H”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 156–161
Citation in format AMSBIB
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