  In this work, for a given inverse semigroup we will define the crossed
product of an inverse semigroup by a partial action. Also, we will associate to
an inverse semigroup $G$ an inverse semigroup $S_G$, and we will prove that
there is a correspondence between the covariant representation of $G$ and
covariant representation of $S_G$. Finally, we will explore a connection
between crossed products of an inverse semigroup actions and crossed products
by partial actions of inverse semigroups.
