Semigroups for which every S-system has the natural partial order

In this note we characterize semigroups S having the property that the relation , defined by x y iff x yS U {y}, partially orders every S-system.Research of second author supported in part by a post-doctoral fellowship in the Biomathematics Program at North Carolina State University under PHS Grant # GM -678 from NIGMS and while on leave from Bowling Green State University.TO ALFRED H. CLIFFORD on his 65th birthday on the 11th of July, 1973