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.

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