Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 775-782
Citer cet article
I. B. Kozhukhov. On potential properties of a semigroup connected with generation of one-sided congruences. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 3, pp. 775-782. http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a10/
@article{FPM_2001_7_3_a10,
author = {I. B. Kozhukhov},
title = {On potential properties of a~semigroup connected with generation of one-sided congruences},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {775--782},
year = {2001},
volume = {7},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a10/}
}
TY - JOUR
AU - I. B. Kozhukhov
TI - On potential properties of a semigroup connected with generation of one-sided congruences
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2001
SP - 775
EP - 782
VL - 7
IS - 3
UR - http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a10/
LA - ru
ID - FPM_2001_7_3_a10
ER -
%0 Journal Article
%A I. B. Kozhukhov
%T On potential properties of a semigroup connected with generation of one-sided congruences
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2001
%P 775-782
%V 7
%N 3
%U http://geodesic.mathdoc.fr/item/FPM_2001_7_3_a10/
%G ru
%F FPM_2001_7_3_a10
A property $P$ is fulfilled potentially in a semigroup $S$ if $P$ is fulfilled in some supersemigroup $T\supseteq S$. We find necessary and sufficient conditions for a given pair $(a,b)$ of elements of $S$ to belong to the right congruence generated by a given set of pairs $(a_i,b_i)$, $i\in I$, potentially. In connection to this we investigate potential solvability of the equation systems of the form $ax=b$, $ax=bx$, $ax=by$.
