LAUSR

We study perfect effect algebras, that is, effect algebras with the Riesz decomposition property where every element belongs either to its radical or to its co-radical. We define perfect effect algebras with principal radical and we show that the category of such effect algebras is categorically equivalent to the category of unital po-groups with interpolation. We introduce an observable on a $$\hbox {Rad}$$Rad-monotone $$\sigma $$σ-complete perfect effect algebra with principal radical and we show that observables are in a one-to-one correspondence with spectral resolutions of observables.