Set-theoretic relations and BCH-algebras with trivial structure


Wiesĺaw Dudek, Ronald Rousseau




In any BCH-algebra we can define a natural relation which is reflexive and anti-symmetric. This relation induces fundamental properties of a BCH-algebra, but not induces the BCH-operation in general. Moreover, some types of BCH-algebras may be obtained from other reflexive and anti-symmetric relations. We describe connections between such relations. We give also some methods of constructions of BCH-algebras from given relations.