Perfect Effect Algebras Are Categorically Equivalent with Abelian Interpolation Po-groups
نویسنده
چکیده
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 this 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 to 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. 2000 Mathematics subject classification: primary 06F20; secondary 03G12, 03B50.
منابع مشابه
THE LEXICOGRAPHIC PRODUCT OF PO-GROUPS AND n-PERFECT PSEUDO EFFECT ALGEBRAS
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