Natural Partial Orders on the Semigroup of Binary Relations

C. Namnak, P. Preechasilp

Abstract

Let B(X) denote the semigroup of binary relations on a set X under composition. We study two natural partial orders on B(X) and characterize when two elements of B(X) are related under these orders. The maximality, minimality, left compatibility and right compatibility of elements are considered with respect to each order.