Semigroups in which the radical of every interior ideal is a subsemigroup

In this paper, we characterize when the radical $\sqrt{I}$ of every interior ideal $I$ of a semigroup $S$ is a subsemigroup of $S$. Also, the radical of every interior ideal (or right ideal or left ideal or quasi-ideal or ideal or bi-ideal or subsemigroup) of $S$ is an interior ideal (or a right ideal or a left ideal or a quasi-ideal or an ideal or a bi-ideal) of $S$.