This article is cited 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.

UDC: 517.977

Received: 22.02.2013

 English version: Proceedings of the Steklov Institute of Mathematics (Supplement Issues), 2014, 287, suppl. 1, S134–S144

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