The next meeting of the Algebra and Logic Seminar will be held

on

**May 17, 2019**(Friday) at**1:00 p.m.**in**Room 578**of the Institute of Mathematics and Informatics.A talk on

## SOME CONGRUENCES ON THE ENDOMORPHISM MONOID OF A PARTICULAR DIGRAPH

will be delivered by

**Laddawan LOHAPAN**(Khon Kaen University, Khon Kaen, Thailand)**.**Everybody is invited.

**Abstract**. As normal subgroups in groups, congruences in Semigroup Theory play an important role. We consider the endomorphism monoid of the directed graph on the set of all natural numbers together with the so-called zig-zag order. The endomorphism monoid on a zig-zag order on $mathbb{N}$ can be regarded as the monoid $O_{mathbb{N}}$ of transformations preserving a zig-zag order. This monoid was first studied by Currie in 1991 and Rutkowski in 1992. In this presentation, we determine all maximal congruences on $O_{mathbb{N}}$ containing a particular equivalence on $O_{mathbb{N}}.$.