ON $π$-EXTENSIONS OF THE SEMIGROUP $Z_+$ - Grigoryan, T.A.; Lipacheva, E.V.; Tepoyan, V.H. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2013)
In the paper inverse $π$-extensions of the semigroup $Z_+$ are studied. It is shown that $π$-extension of the semigroup $Z_+$ is inverse, if and only if its $π$-extension coincides with $p(Z_+)$. The existence of a non-inverse $π$-extension for any abelian semigroup is proved.
Keywords: inverse semigroup; inverse representation; $π$-extension; Toeplitz algebra; inverse $π$-extension; $C^*$-algebra