On regularity of semigroups of maps that preserve a~binary relation
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 225-240
Voir la notice de l'article provenant de la source Math-Net.Ru
We consider semigroups of full transformations, partial maps, and multi-value maps from a set $X$ to $X$, where every map preserves a binary relation $\sigma$ defined on $X$. We suggest several definitions for the preservation of $\sigma$ for partial maps and for multi-value maps. We review results about regularity of the semigroups mentioned above in the cases where $\sigma$ is a partial order, a quasi-order, an equivalence, or one of some special kinds of binary relations. Also we consider the question about regularity of the semigroup of full transformations that preserve a partial order and an equivalence simultaneously.
@article{FPM_2021_23_4_a12,
author = {V. A. Yaroshevich},
title = {On regularity of semigroups of maps that preserve a~binary relation},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {225--240},
publisher = {mathdoc},
volume = {23},
number = {4},
year = {2021},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a12/}
}
V. A. Yaroshevich. On regularity of semigroups of maps that preserve a~binary relation. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 225-240. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a12/