Abstract: Let S be a ring, and H(S) be the quaternion ring on S. We consider the (m,n)-Jordan centralizers and (m,n)-Lie centralizers on the quaternion ring. By using the generator analysis method, we prove that the (m,n)-Jordan centralizers are standard centralizers, a
nd the (m,n)-Lie centralizers are standard Lie centralizers.

Key words: quaternion ring, (m,n)-Jordan centralizer, (m,n)-Lie centralizer