Komarnytskyi Scientific Seminar
at Algebra & Logic and Geometry & Topology Departments of
Ivan Franko National University of Lviv
Archive for (2017/2018) academic year

S-acts Theory and
Spectral Spaces

September 14, 2017 All participants
November 2, 2017 A. Savchuk
November 9, 2017 A. Savchuk
November 23, 2017 A. Savchuk
November 30, 2017 P. Khylynskyi
December 7, 2017 P. Khylynskyi
December 19, 2017 All participants
December 28, 2017 A. Ravsky
April 17, 2018 O. Gutik
  • On group congruences of inverse semigroups whose contain the semigroup of partial co-finite isometries of positive integers, III
    • Let $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ be the the semigroup of cofinite monotone partial bijections of the set of pusitive integers $\mathbb{N}$ and $\mathbf{I}\mathbb{N}_{\infty}$ be the semigroup of all partial co-finite isometries of $\mathbb{N}$. We give a criterium when an inverse subsemigroup $S$ of $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathbf{I}\mathbb{N}_{\infty}$ has the following property: every non-identity congruence of $S$ is a group congrunce. We describe minimal inviverse subsemigroups with such property.

April 25, 2018 O. Gutik
  • On variants of the bicyclic extended semigroup
    • 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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