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 $T \supseteq S$. 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 (ai,bi), $i \in I$, potentially. In connection to this we investigate potential solvability of the equation systems of the form ax=b, ax=bx, ax=by.

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Last modified: December 23, 2001