Scientific Seminar
at Geometry and Topology Department of
Ivan Franko National University of Lviv
Archive for (2017/2018) academic year



Topological
Algebra

September 14, 2017 All participants
September 27, 2017 M. Khylynskyi
  • On the λ-polycyclic estension of a monoid
    • We introduce the λ-polycyclic estension of a monoid and discuss its properties.

October 4, 2017 M. Khylynskyi
  • On the λ-polycyclic estension of a monoid, II
    • We introduce the λ-polycyclic estension of a monoid and discuss its algebraic properties.

October 18, 2017 T. Mokrytskyi
  • The monoid $\mathcal{IPF}(\mathbb{N}^n)$ of order isomorphisms of principal filters of a power of the positive integers

    • Let $n$ be any positive integer and $\mathcal{IPF}(\mathbb{N}^n)$ be the semigroup of all order isomorphisms between principal filters of the $n$-th power of the set of positive integers $\mathbb{N}$ with the product order. We study algebraic properties of the semigroup $\mathcal{IPF}(\mathbb{N}^n)$. In particular, we show that $\mathcal{IPF}(\mathbb{N}^n)$ bisimple inverse semigroup, describe Green's relations on $\mathcal{IPF}(\mathbb{N}^n)$ and its maximal subgroups. We prove that every non-identity congruence $\mathfrak{C}$ on the semigroup $\mathcal{IPF}(\mathbb{N}^n)$ is group.

October 25, 2017 T. Mokrytskyi
  • The monoid $\mathcal{IPF}(\mathbb{N}^n)$ of order isomorphisms of principal filters of a power of the positive integers, II

    • Let $n$ be any positive integer and $\mathcal{IPF}(\mathbb{N}^n)$ be the semigroup of all order isomorphisms between principal filters of the $n$-th power of the set of positive integers $\mathbb{N}$ with the product order. We study algebraic properties of the semigroup $\mathcal{IPF}(\mathbb{N}^n)$. In particular, we show that $\mathcal{IPF}(\mathbb{N}^n)$ bisimple inverse semigroup, describe Green's relations on $\mathcal{IPF}(\mathbb{N}^n)$ and its maximal subgroups. We prove that every non-identity congruence $\mathfrak{C}$ on the semigroup $\mathcal{IPF}(\mathbb{N}^n)$ is group.

November 1, 2017 A. Ravsky
  • A few open problems from Mathematics StackExchange

November 8, 2017 O. Sobol
November 15, 2017 O. Sobol
November 22, 2017 O. Sobol
November 29, 2017 O. Sobol
December 6, 2017 S. Bardyla
  • On topological semilattices with compact maximal chains

    • We investigate topological semilattices with compact maximal chains. In particular, we prove that a topological semilattice X is multiclosed in the class of topological semigroups iff X is a semilattice with compact maximal chains. Some open problems will be posed.

December 13, 2017 S. Bardyla
  • On topological semilattices with compact maximal chains, II

    • We investigate topological semilattices with compact maximal chains. In particular, we prove that a topological semilattice X is multiclosed in the class of topological semigroups iff X is a semilattice with compact maximal chains. Some open problems will be posed.

December 19, 2017 All participants
January 3, 2018 S. Bardyla
  • On topological semilattices with compact maximal chains, III

    • We investigate topological semilattices with compact maximal chains. In particular, we prove that a topological semilattice X is multiclosed in the class of topological semigroups iff X is a semilattice with compact maximal chains. Some open problems will be posed.