A study on semigroups in which the radical of every n-interior ideal is a subsemigroup

The radical of a nonempty set is a set that corresponds to some properties. There are many methods to study a semigroup such as the connections between their ideals of such a semigroup. In this paper, we consider the semigroup with identity element and characterize when the radical of every [Formula: see text]-interior ideal of a semigroup is a subsemigroup of such a semigroup. We also characterize that the radical of every [Formula: see text]-interior ideal (right ideal, left ideal, two-sided ideal, [Formula: see text]-ideal, quasi-ideal, [Formula: see text]-quasi-ideal, bi-ideal, [Formula: see text]-interior ideal) of a semigroup is an [Formula: see text]-interior ideal of semigroups.