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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 4, Pages 181–191
(Mi timm1012)
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This article is cited in 2 scientific papers (total in 2 papers)
The structure of finite monoids satisfying the relation $\mathscr{R}=\mathscr{H}$
T. V. Pervukhina Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg
Abstract:
It is shown that any finite monoid $S$ on which Green's relations $\mathscr{R}$ and $\mathscr{H}$ 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 $\mathscr{R}=\mathscr{H}$ with the semidirect product of the pseudovariety of all finite groups and the pseudovariety of all finite $\mathscr{R}$-trivial monoids.
Keywords:
finite monoids, Green’s relations, monoid representation, monoid pseudovariety, upper-triangular matrices.
Received: 22.02.2013
Citation:
T. V. Pervukhina, “The structure of finite monoids satisfying the relation $\mathscr{R}=\mathscr{H}$”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 4, 2013, 181–191; Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 134–144
Linking options:
https://www.mathnet.ru/eng/timm1012 https://www.mathnet.ru/eng/timm/v19/i4/p181
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Abstract page: | 165 | Full-text PDF : | 64 | References: | 33 | First page: | 2 |
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