On $\pi$-extensions of the semigroup ${\mathbb{Z}}_{+}$

Abstract

We study inverse $\pi$-extensions of the semigroup ${\mathbb{Z}}_{+}$. It is shown that $\pi$-extension of the semigroup ${\mathbb{Z}}_{+}$ is inverse, iff its $\pi$-extension coincides with $\pi ({\mathbb{Z}}_{+})$. The existence of a non-inverse $\pi$-extension for semigroup ${\mathbb{Z}}_{+}$ is proved.

Short communication, 3 pages