
{\bf Perfect effect algebras  are categorically equivalent  with Abelian interpolation  po-groups}

{\it Anatolij Dvure{\v c}enskij}


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ABSTRACT:

We introduce perfect effect algebras and we show that every
perfect algebra is an interval in the lexicographical
product of the group of all  integers with an Abelian
directed interpolation po-group. To show that we introduce
prime ideals of effect algebras with the Riesz decomposition
property, (RDP). We show that the category of perfect effect
algebras is categorically equivalent with the category of
Abelian directed interpolation po-groups. Moreover, we prove
that any perfect effect algebra is a subdirect product of
antilattice effect algebras with the (RDP).


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{\it AMS classification (1991): }
06F20, 03G12, 03B50

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{\it Keywords: }
effect algebra, the Riesz decomposition property, radical, perfect effect algebra, interpolation po-group, unital po-group, categorical equivalence

