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Perfect effect algebras are categorically equivalent with abelian interpolation po-groups. (English) Zbl 1117.06009
The author introduces “perfect effect algebras” and shows that the category of perfect effect algebras is equivalent to the category of partially ordered abelian groups whose order is directed and has the Riesz decomposition property. It is also shown that every perfect effect algebra is a subdirect product of antilattice effect algebras with the Riesz decomposition property.

06D35 MV-algebras
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
03G12 Quantum logic
03B50 Many-valued logic
Full Text: DOI
[1] Dvurečenskij, New trends in quantum structures (2000)
[2] Di Nola, Port. Math. 50 pp 87– (1993)
[3] DOI: 10.1007/BF01057937 · Zbl 0812.06010
[4] DOI: 10.2307/1993227 · Zbl 0084.00704
[5] Lane, Categories for the working mathematician (1971) · Zbl 0232.18001
[6] DOI: 10.1023/A:1004144832348 · Zbl 0994.81009
[7] Kôpka, Math. Slovaca 44 pp 21– (1994)
[8] Glass, Partially ordered groups (1999) · Zbl 0933.06010
[9] Fuchs, Partially ordered algebraic systems (1963) · Zbl 0137.02001
[10] DOI: 10.1007/BF02283036 · Zbl 1213.06004
[11] Goodearl, Partially ordered abelian groups with interpolation (1986) · Zbl 0589.06008
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