The separator of a subset of a semigroup
In this paper we introduce a new notion by the help of the idealizer. This new notion is the separator of a subset of a semigroup. We investigate the properties of the separator in an arbitrary semigroup and characterize the unitary subsemigroups and the prime ideals by the help of their separator. The last section of this paper treats the separator of a free subsemigroup of a free semigroup.