Narrow Results

Firstly, we show that the variety of all left(right) regular bands and the variety of all normal bands are closed in the variety of all left(right) semiregular bands and the variety of all medial semigroups, respectively. Then, we show that the class of all regular medial semigroups satisfying certain condition is absolutely closed.

In this paper, we prove that the dominion of any full orthodox subsemigroup of a medial orthodox semigroup is described by the Isbell zigzag theorem in the category of medial orthodox semigroups. As a consequence, the dominions of any full completely regular subsemigroup of a medial completely regular semigroup as well as that of any full Clifford subsemigroup of a medial Clifford semigroup are also described by the Isbell zigzag theorem in the categories of all medial completely regular semigroups and of all medial Clifford semigroups, respectively.