On V n -semigroups
In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced. Also, we give a characterization of Vn-semigroups and investigate some properties of Vn-semigroups. Furthermore, we show that the class of Vn-semigroups is closed under direct products and homomorphic images. However, regular subsemigroups of Vn-semigroups (n ≥ 2) are not necessarily Vn-semigroups...