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

View as HTML
View as gif image
View as LaTeX source

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.

Location: http://mech.math.msu.su/~fpm/eng/k01/k013/k01311h.htm

Last modified: December 23, 2001