

September 14, 2017

All participants




September 27, 2017

M. Khylynskyi


On the λpolycyclic estension of a monoid

We introduce the λpolycyclic estension of a monoid and discuss its properties.



October 4, 2017

M. Khylynskyi


On the λpolycyclic estension of a monoid, II

We introduce the λpolycyclic 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 nonidentity 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 nonidentity 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


Syntactic semigroup problem for the semigroup reducts
of affine nearsemirings over Brandt semigroups



November 15, 2017

O. Sobol


Syntactic semigroup problem for the semigroup reducts
of affine nearsemirings over Brandt semigroups, II



November 22, 2017

O. Sobol


Syntactic semigroup problem for the semigroup reducts
of affine nearsemirings over Brandt semigroups, III



November 29, 2017

O. Sobol


On some reuslts of J. Kumar and K. V. Krishna

We give a survey on the resuls of the papers: [J. Kumar and K. V. Krishna, Affine NearSemirings Over Brandt Semigroups,
Communications in Algebra 42, No. 12 (2014) 52525169], [J. Kumar and K. V. Krishna, Rank Properties of Multiplicative Semigroup Reduct of Affine NearSemirings over $B_n$,
arXiv:1311.0789v2], [J. Kumar and K. V. Krishna, The Ranks of the Additive Semigroup Reduct of Affine NearSemiring over Brandt Semigroup,
arXiv:1308.4087v1], [J. Kumar and K. V. Krishna, Syntactic semigroup problem for the semigroup reducts
of affine nearsemirings over Brandt semigroups, AsianEur. J. Math. 9, No. 1 (2016) 1650021 (10 pages)], [J. Kumar and K. V. Krishna, Radicals and Ideals of Affine NearSemirings Over Brandt Semigroups, Romeo P., Meakin J., Rajan A. (eds), Semigroups, Algebras and Operator Theory. Springer Proceedings in Mathematics & Statistics, vol 142. Springer, New Delhi, pp 123133] and [J. Kumar and K. V. Krishna, Rank properties of the semigroup reducts of affine nearsemirings over Brandt semigroups,
Semigroup Forum 93, No. 3 (2014) 516534].



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.



January 24, 2018

A. Ravsky


Two new algebra working problems, II



February 14, 2018

O. Sobol,
O. Gutik


On feebly compact semitopological semilattice $\exp_n\lambda$

We discuss on feebly compact shiftcontinous topologies $\tau$ on the semilattice $\left(\exp_n\lambda,\cap\right)$. It is proved that for any shiftcontinuous $T_1$topology $\tau$ on $\exp_n\lambda$ the following conditions are equivalent:
$(i)$ $\tau$ is countably pracompact; $(ii)$ $\tau$ is feebly compact; $(iii)$ $\tau$ is $d$feebly compact; $(iv)$~$\left(\exp_n\lambda,\tau\right)$ is an $H$closed space;
$(v)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially countably pracompact;
$(vi)$~$\left(\exp_n\lambda,\tau\right)$ is selectively sequentially feebly compact;
$(vii)$~$\left(\exp_n\lambda,\tau\right)$ is selectively feebly compact;
$(viii)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially feebly compact;
$(ix)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathfrak{D}(\omega)$compact;
$(x)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathbb{R}$compact;
$(xi)$~$\left(\exp_n\lambda,\tau\right)$ is infra Hclosed.



February 21, 2018

O. Sobol,
O. Gutik


On feebly compact semitopological semilattice $\exp_n\lambda$, II

We discuss on feebly compact shiftcontinous topologies $\tau$ on the semilattice $\left(\exp_n\lambda,\cap\right)$. It is proved that for any shiftcontinuous $T_1$topology $\tau$ on $\exp_n\lambda$ the following conditions are equivalent:
$(i)$ $\tau$ is countably pracompact; $(ii)$ $\tau$ is feebly compact; $(iii)$ $\tau$ is $d$feebly compact; $(iv)$~$\left(\exp_n\lambda,\tau\right)$ is an $H$closed space;
$(v)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially countably pracompact;
$(vi)$~$\left(\exp_n\lambda,\tau\right)$ is selectively sequentially feebly compact;
$(vii)$~$\left(\exp_n\lambda,\tau\right)$ is selectively feebly compact;
$(viii)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially feebly compact;
$(ix)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathfrak{D}(\omega)$compact;
$(x)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathbb{R}$compact;
$(xi)$~$\left(\exp_n\lambda,\tau\right)$ is infra Hclosed.



March 14, 2018

A. Savchuk,
O. Gutik


The semigroup of partial cofinite isometries of positive integers

The semigroup $\mathbf{I}\mathbb{N}_{\infty}$ of all partial cofinite isometries of positive integers is discussed. We describe the Green relations on the semigroup $\mathbf{I}\mathbb{N}_{\infty}$, its band and proved that $\mathbf{I}\mathbb{N}_{\infty}$ is a simple $E$unitary $F$inverse semigroup. It is described the least group congruence $\mathfrak{C}_{\mathbf{mg}}$ on $\mathbf{I}\mathbb{N}_{\infty}$ and proved that the quotientsemigroup $\mathbf{I}\mathbb{N}_{\infty}/\mathfrak{C}_{\mathbf{mg}}$ is isomorphic to the additive group of integers $\mathbb{Z}(+)$. An example of a nongroup congruence on the semigroup $\mathbf{I}\mathbb{N}_{\infty}$ is presented.



March 21, 2018

O. Gutik


The semigroup of partial cofinite isometries of positive integers, II

The semigroup $\mathbf{I}\mathbb{N}_{\infty}$ of all partial cofinite isometries of positive integers is discussed. We proved that a congruence on the semigroup
$\mathbf{I}\mathbb{N}_{\infty}$ is group if and only if its restriction onto an isomorphic copy of the bicyclic semigroup in $\mathbf{I}\mathbb{N}_{\infty}$ is a group congruence.



March 28, 2018

O. Gutik


On group congruences of inverse semigroups whose contain the semigroup of partial cofinite isometries of positive integers

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 cofinite 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 nonidentity
congruence of $S$ is a group congrunce. We describe minimal inviverse subsemigroups with such property.



April 4, 2018

L. Plachta


On mesures of nonplanarity of cubic graphs

We study two measures of nonplanarity of cubic graphs $G$, the genus
$\gamma(G)$ and the edge deletion number $\mathbf{ed}(G)$. For cubic graphs of
small order these
parameters are compared with another measure of
nonplanarity, the (rectiliniar) crossing number $\overline{\mathbf{cr}}(G)$. We
introduce operations of connected sum,
specified for cubic graphs $G$,
and show that under certain conditions the parameters $\gamma(G)$ and
$ed(G)$ are additive (subadditive) with respect to them.
The minimal genus graphs (i.e. the cubic graphs of minimum order with
given value of genus $\gamma$) and the minimal edge deletion graphs
(i.e. cubic graphs of minimum
order with given value of edge deletion
number $\mathbf{ed}$) are introduced and studied. We provide upper bounds for the order
of minimal genus and minimal edge deletion graphs.



April 11, 2018

O. Gutik


On group congruences of inverse semigroups whose contain the semigroup of partial cofinite isometries of positive integers, II

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 cofinite 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 nonidentity
congruence of $S$ is a group congrunce. We describe minimal inviverse subsemigroups with such property.



April 18, 2018

S. Bardyla


Embedding of graph inverse semigroups into compactlike topological semigroups

We investigate graph inverse semigroups which are subsemigroups of compactlike topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into dcompact topological semigroups.



April 25, 2018

S. Bardyla


Embedding of graph inverse semigroups into compactlike topological semigroups, II

We investigate graph inverse semigroups which are subsemigroups of compactlike topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into dcompact topological semigroups.



May 2, 2018

S. Bardyla


Embedding of graph inverse semigroups into compactlike topological semigroups, III

We investigate graph inverse semigroups which are subsemigroups of compactlike topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into dcompact topological semigroups.



May 16, 2018

S. Bardyla


Embedding of graph inverse semigroups into compactlike topological semigroups, IV

We investigate graph inverse semigroups which are subsemigroups of compactlike topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into dcompact topological semigroups.



July 19, 2018

A. Ravsky


On the Koch problem

We discuss on Koch's problem. In particular, we give a positive answer on Koch's problem in some partial cases.

