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Komarnytskyi Scientific Seminar:

S-acts Theory and Spectral Spaces
Founded by Prof. M. Komarnyts'kyy & O. Gutik in 2010

Науковий семінар ім. М. Комарницького:

Теорія полігонів i спектральні простори

Заснований Проф. M. Koмaрницьким & O. Гутіком у 2010 році

Speaker: Oleg Gutik

Talk: On variants of the bicyclic extended semigroup, II
When & where: May 2, 2018, 13 30 at room 149 a

We describe the group $\mathbf{Aut}\left(\mathcal{C}_{\mathbb{Z}}\right)$ of automorphisms of the extended bicyclic semigroup $\mathcal{C}_{\mathbb{Z}}$ and study variants $\mathcal{C}_{\mathbb{Z}}^{m,n}$ of the extended bicycle semigroup $\mathcal{C}_{\mathbb{Z}}$, where $m,n\in\mathbb{Z}$. Especially we prove that $\mathbf{Aut}\left(\mathcal{C}_{\mathbb{Z}}\right)$ is isomorphic to the additive group of integers and describe the subset of idempotents $E(\mathcal{C}_{\mathbb{Z}}^{m,n})$ and Green's relations of the semigroup $\mathcal{C}_{\mathbb{Z}}^{m,n}$. Also we show that $E(\mathcal{C}_{\mathbb{Z}}^{m,n})$ is an $\omega$-chain and any two variants of the extended bicyclic semigroup $\mathcal{C}_{\mathbb{Z}}$ are isomorphic.

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