Every effect algebra can be made into a total algebra

Every effect algebra can be made into a total algebra

We prove that every effect algebra ( E ,+, 0, 1) can easily be made into a total algebra ( E ,⊕, ¬, 0) of type (2, 1, 0) in such a way that two elements are compatible in ( E ,+, 0, 1) if and only if they commute in ( E ,⊕, ¬, 0).

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Veröffentlicht in:Algebra universalis 2009-11, Vol.61 (2), p.139-150
Hauptverfasser: Chajda, I., Halaš, R., Kühr, J.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Mathematics
Mathematics and Statistics
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Zusammenfassung:We prove that every effect algebra ( E ,+, 0, 1) can easily be made into a total algebra ( E ,⊕, ¬, 0) of type (2, 1, 0) in such a way that two elements are compatible in ( E ,+, 0, 1) if and only if they commute in ( E ,⊕, ¬, 0).
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-009-0010-6