FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 7, PAGES 129-

**Transformation semigroups preserving a binary relation**

I. B. Kozhukhov

V. A. Yaroshevich

Abstract

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We investigate the semigroups of full and partial transformations of
a set $X$ which preserve
a binary relation $$s defined
on $X$.
We consider in detail the case where $$s is an order or
a quasi-order relation.
There are conditions of regularity of such semigroups.
We introduce two definitions of preservation of $$s for the semigroup of
binary relations.
It is proved that subsets of $B(X)$
preserving $$s are semigroups in
each case.
We give the condition of regularity of $B$_{s}(X) in the case
where $$s (X) is
a quasi-order.

Location: http://mech.math.msu.su/~fpm/eng/k08/k087/k08710h.htm

Last modified: June 25, 2009