# Ivan-Vanja Boroja: Compression of the commuting graph of rings

In this talk we will present some result of collaboration between Banja Luka and Ljubljana. We will discuss the standard commuting graph and its compression. The compression is chosen in such a way that it induces a functor from the category of rings to the category of graphs, which means that the compressed commuting graph takes into account not only the commutativity relation in the ring, but also the commutativity relation in all of its homomorphic images. We show that this compression is best possible for matrix algebras over finite fields and describe the graph of finite fields and of rings of 2x2 matrices over finite fields. We will also discuss when the compressed commuting graph of an infinite ring is finite.

Vljudno vabljeni. Roman Drnovšek in Primož Moravec