Özet:
Let S be a finite semigroup and let ? be an aquivalence relation on S such that ? is a congruence. Then ? is a subsemigroup of S, the direct product of semigroups, and S/?={x?:x?S} is a semigroup with (x?)(y?)=(xy)?. In [2,3] Howie and Ribeiro study the small, lower, intermediate, upper and large rank of a finite semigroups S. In this paper, we investigate some relation among ranks of semigroups S, ? and S/?.