Geodesic
On $\pi$-extensions of the semigroup $\mathbb{Z}_+$
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2013), pp. 3-5

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In the paper inverse $\pi$-extensions of the semigroup $\mathbb{Z}_+$ are studied. It is shown that $pi$-extension of the semigroup $\mathbb{Z}_+$ is inverse, if and only if its $\pi$-extension coincides with $\pi(\mathbb{Z}_+)$. The existence of a non-inverse $\pi$-extension for any abelian semigroup is proved.
Keywords: inverse semigroup, inverse representation, $\pi$-extension, Toeplitz algebra, $C^*$-algebra, inverse $\pi$-extension. 
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T. A. Grigoryan; E. V. Lipacheva; V. H. Tepoyan. On $\pi$-extensions of the semigroup $\mathbb{Z}_+$. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2013), pp. 3-5. http://geodesic.mathdoc.fr/item/UZERU_2013_1_a0/