Geodesic
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
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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 $ax=b$, $ax=bx$, $ax=by$. 
@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/}
}
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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/