On congruence permutable $G$-sets

Nagy, Attila. "On congruence permutable $G$-sets." Commentationes Mathematicae Universitatis Carolinae 61.2 (2020): 139-145. <http://eudml.org/doc/297023>.

@article{Nagy2020,
abstract = {An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha $ and $\beta $ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha $, where $\circ $ denotes the usual composition of binary relations. To an arbitrary $G$-set $X$ satisfying $G\cap X=\emptyset $, we assign a semigroup $(G,X,0)$ on the base set $G\cup X\cup \lbrace 0\rbrace $ containing a zero element $0\notin G\cup X$, and examine the connection between the congruence permutability of the $G$-set $X$ and the semigroup $(G,X,0)$.},
author = {Nagy, Attila},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$G$-set; congruence permutable algebras; semigroup},
language = {eng},
number = {2},
pages = {139-145},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On congruence permutable $G$-sets},
url = {http://eudml.org/doc/297023},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Nagy, Attila
TI - On congruence permutable $G$-sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 2
SP - 139
EP - 145
AB - An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha $ and $\beta $ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha $, where $\circ $ denotes the usual composition of binary relations. To an arbitrary $G$-set $X$ satisfying $G\cap X=\emptyset $, we assign a semigroup $(G,X,0)$ on the base set $G\cup X\cup \lbrace 0\rbrace $ containing a zero element $0\notin G\cup X$, and examine the connection between the congruence permutability of the $G$-set $X$ and the semigroup $(G,X,0)$.
LA - eng
KW - $G$-set; congruence permutable algebras; semigroup
UR - http://eudml.org/doc/297023
ER -