On Q-regular semigroups

In this paper, we give some characterizations of Q-regular semigroups and show that the class of Q-regular semigroups is closed under the direct product and homomorphic images. Furthermore, we characterize the Q-subdirect products of this class of semigroups and study the -unitary Q-regular covers for Q-regular semigroups, in particular for those whose maximum group homomorphic image is a given group. As an application of these results, we claim that the similar results on -regular semigroups also hold.