FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 3, PAGES 775-782

On potential properties of a semigroup connected with generation of one-sided congruences

I. B. Kozhukhov

Abstract

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A property $P$ is fulfilled potentially in a semigroup $S$ if $P$ is fulfilled in some supersemigroup $\$T\; \backslash supseteq\; S\$$. 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), $\$i\; \backslash in\; I\$$, potentially. In connection to this we investigate potential solvability of the equation systems of the form $ax=b$, $ax=bx$, $ax=by$.

All articles are published in Russian.

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Last modified: December 23, 2001