On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup

It is proved that the semigroups $\mathbf{E}\mathbf{n}\mathbf{d}({\mathit{B}}_{\omega })$ and $\mathbf{E}\mathbf{n}\mathbf{d}({\mathit{B}}_{\mathbb{Z}})$ of the endomorphisms of the bicyclic semigroup ${\mathit{B}}_{\omega }$ and the endomorphisms of the extended bicyclic semigroup ${\mathit{B}}_{\mathbb{Z}}$ are isomorphic to the semidirect products $(\omega ,+){⋊}_{\phi }(\omega ,\ast )$ and $\mathbb{Z}(+){⋊}_{\phi }(\omega ,\ast )$, respectively.