Measures on Pseudo-BCK Algebras
In this chapter we generalize the measures on BCK-algebras introduced by Dvurečenskij and Pulmannova, to pseudo-BCK algebras that are not necessarily bounded. In particular, we show that if A is a downwards-directed pseudo-BCK algebra and m a measure on it, then the quotient over the kernel of m can be embedded into the negative cone of an Abelian, Archimedean ℓ-group as its subalgebra. This result will enable us to characterize nonzero measure-morphisms as measures whose kernel is a maximal deductive system.
KeywordsBorel Measure Weak Topology Deductive System Borel Probability Measure Negative Cone
- 208.Kühr, J.: Pseudo-BCK algebras and related structures. Univerzita Palackého v Olomouci (2007) Google Scholar