A characterization of cone preserving mappings of quasiordered sets. (English) Zbl 1095.08001

Chajda, Ivan; Hošková, Šárka

Miskolc Math. Notes 6, No. 2, 147-152 (2005).

Summary: A cone of a quasiordered set \((A,Q)\) is any \(U_Q(a)=\{x\in A : \langle a,x\rangle \in Q\}\). A mapping \(f: A\to B\) is a cone preserving mapping of \((A,Q)\) into \((B,Q')\) if \(f(U_Q(a))=U_{Q'}(f(a))\) for each \(a\in A\). We characterize these mappings by using certain relational inclusions. The result can be applied for the construction of a quotient quasiorder hypergroup.

MSC:

08A02	Relational systems, laws of composition
08A30	Subalgebras, congruence relations
20N20	Hypergroups

Keywords:

quasiorder; quasiorder hypergroup; factorization of quasiordered set; quotient hypergroup