ON $\pi$-EXTENSIONS OF THE SEMIGROUP $Z_+$

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

doi:10.46991/PYSU:A/2013.47.1.003

ON $\pi$-EXTENSIONS OF THE SEMIGROUP $Z_+$

Authors

T.A. Grigoryan Kazan State Power Engineering University, Russian Federation
E.V. Lipacheva Kazan State Power Engineering University, Russian Federation
V.H. Tepoyan Chair of Differential Equations, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2013.47.1.003

Keywords:

inverse semigroup, inverse representation, $\pi$-extension, Toeplitz algebra, inverse $\pi$-extension, $C^*$-algebra

Abstract

In the paper inverse $\pi$-extensions of the semigroup $Z_+$ are studied. It is shown that $\pi$-extension of the semigroup $Z_+$ is inverse, if and only if its $\pi$-extension coincides with $p(Z_+)$. The existence of a non-inverse $\pi$-extension for any abelian semigroup is proved.

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Published

2013-04-10

How to Cite

Grigoryan, T., Lipacheva, E., & Tepoyan, V. (2013). ON $\pi$-EXTENSIONS OF THE SEMIGROUP $Z_+$. Proceedings of the YSU A: Physical and Mathematical Sciences, 47(1 (230), 3–5. https://doi.org/10.46991/PYSU:A/2013.47.1.003