A note on effect algebras and dimension theory of AF C*-algebras

We continue in the investigation of the relations between effect algebras and AF C*-algebras started by Pulmannovل, 1999. In particular, in analogy with the notion of a dimension group, we introduce the notion of a di mension effect algebra as an effect algebra obtained as the direct limit of finite effect algebras with RDP. We also give an intrinsic characterization of dimension effect algebras. It turns out that every dimension effect algebra is a unit interval in a dimension group with a unit. We prove that there is a categorical equivalence between the category of countable dimension effect algebras and unital AF C*-algebras.