Abstract:
Perfect pseudo effect algebras are introduced, and ideals,maximal ideals,prime ideals and values are defined. It is proved that every value in a pseudo effect algebra has a cover,the set of all ideals is a distributive lattice. The definition of an infinitesimal element is introduced,and some conditions for the set Infinit(E) be equal to the intersection Rad(E) of all maximal ideals are obtained, it is proved there exists a faithful and full functor from the category of directed interpolation po-groups GI into the category of perfect pseudo effect algebras PPEA and every perfect pseudo effect algebra is an interval in the lexicographical product of the group of all integers with a directed interpolation po-group.
