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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TIMM_2015_21_1_a19,
     author = {T. V. Pervukhina},
     title = {Characterization of the pseudovariety generated by finite monoids satisfying $\mathscr{R}=\mathscr{H}$},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {197--204},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a19/}
}
TY  - JOUR
AU  - T. V. Pervukhina
TI  - Characterization of the pseudovariety generated by finite monoids satisfying $\mathscr{R}=\mathscr{H}$
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2015
SP  - 197
EP  - 204
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a19/
LA  - ru
ID  - TIMM_2015_21_1_a19
ER  - 
%0 Journal Article
%A T. V. Pervukhina
%T Characterization of the pseudovariety generated by finite monoids satisfying $\mathscr{R}=\mathscr{H}$
%J Trudy Instituta matematiki i mehaniki
%D 2015
%P 197-204
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a19/
%G ru
%F TIMM_2015_21_1_a19
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/