Congruences in transitive relational systems
Ivan Chajda · Miskolc mathematical notes/Mathematical notes · 2004
A. A transitive relational system means a pair (A, R) where A∅ and R is a transitive binary relation on A. We define a congruence θ on (A, R) and a factor relation R/θ on the factor set A/θ such that the factor system (A/θ, R/θ) is also a transitive relational system.We show that these congruences are in a one-toone correspondence with the so-called LU-morphisms whenever the relation R is a quasiorder on A.