A PARTIAL ORDER ON TRANSFORMATION SEMIGROUPS THAT PRESERVE DOUBLE DIRECTION EQUIVALENCE RELATION
Lei Sun, Junling Sun · Journal of Algebra and Its Applications · 2013
Let [Formula: see text] be the full transformation semigroup on a nonempty set X and E be an equivalence relation on X. Then [Formula: see text] is a subsemigroup of [Formula: see text]. In this paper, we endow it with the natural partial order. With respect to this partial order, we determine when two elements are related, find the elements which are compatible and describe the maximal (minimal) elements. Also, we investigate the greatest lower bound of two elements.