## Congruences in transitive relational systems.(English)Zbl 1047.08001

Summary: A transitive relational system is a pair $$(A,R)$$ where $$A \not = \emptyset$$ and $$R$$ is a transitive binary relation on $$A$$. We define a congruence $$\theta$$ on $$(A,R)$$ and a factor relation $$R / \theta$$ on the factor set $$A / \theta$$ such that the factor system $$(A / \theta,R / \theta)$$ is also a transitive relational system. We show that these congruences are in a one-to-one correspondence with the so-called LU-morphisms whenever the relation $$R$$ is a quasiorder on $$A$$.

### MSC:

 08A02 Relational systems, laws of composition 08A30 Subalgebras, congruence relations