Mathematics

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

T. A. Grigoryan, E. V. Lipacheva, V. H. Tepoyan

Kazan State Power Engineering University, Russian Federation

Abstract: 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.

MSC: 46L05,20M18

Received: 29.09.2012
Accepted: 31.10.2012

Language: English