Serhii Bardyla

Algebraically closed semigroups

In this talk we shall discuss algebraic properties of a semigroup X which ensure that X is absolutely closed in the classes \mathsf T_{\!z}\mathsf S, \mathsf T_{2}\mathsf S and \mathsf T_{1}\mathsf S of Tychonoff zero-dimensional, Hausdorff and T_1 topological semigroups, respectively. These properties are related to the order structure of semilattices, different sorts of boundedness, Zariski topologies and topologizability of semigroups. Also, we present some applications of algebraically closed semigroups.

[1] T. Banakh, S. Bardyla, Characterizing categorically closed commutative semigroups, Journal of Algebra 591 (2022), 84-110.
[2] T. Banakh, S. Bardyla, Categorically closed countable semigroups, preprint, arXiv:2111.14154.

The work of the speaker is supported by the Austrian Science Fund FWF (Grant  M 2967)