
{\bf Product effect algebras}

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


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ABSTRACT:

We introduce a product  on an effect algebra. We prove that
every product effect algebra with the Riesz decomposition
property, (RDP), is an interval in an Abelian unital
interpolation po-ring, and we show that the category of
product effect algebras with the (RDP) is categorically
equivalent with the category of unital Abelian interpolation
po-rings. In addition, we show that every product effect
algebra with the (RDP) and  with $1$ as a product unity is a
subdirect product of antilattice product 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, product effect algebra, po-ring, perfect effect algebra, categorical equivalence

