We study the Riesz Decomposition Property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed to a comparable system of non-void slices indexed by some subgroup of rea
l numbers. Finally, we present their representation by the lexicographic product.
We present a complete characterization of subdirectly irreducible MV-algebras with internal states (SMV-algebras). This allows us to classify subdirectly irreducible state morphism MV-algebras (SMMV-algebras) and describe single generators of the var
iety of SMMV-algebras, and show that we have a continuum of varieties of SMMV-algebras.
