Abstract
The purpose of this note is to introduce primitive ideals of semigroups
and study some topological aspects of the corresponding structure spaces.
We show that every structure space of a semigroup is T0, quasi-compact,
and every nonempty irreducible closed subset has a unique generic point.
Moreover, such a structure space is Hausdorff if and only if every primitive
ideal of the semirgroup is minimal. Finally, we define continuous maps
between structure spaces of semigroups.