On representations of commutative BCK-algebras. (English) Zbl 0942.06009
A commutative BCK-algebra has the relative cancellation property if for \(x,y\geq a\), \(x*a= y*a\) implies that \(x=y\). Any upwards directed commutative BCK-algebra has this property. The authors consider imbeddings of such algebras into Abelian lattice-ordered groups, and universal groups for the BCK-clans derived from the BCK-algebras.
Reviewer: C.S.Hoo (Edmonton)
MSC:
06F35 | BCK-algebras, BCI-algebras |
03G12 | Quantum logic |
06F20 | Ordered abelian groups, Riesz groups, ordered linear spaces |