Total extensions of effect algebras

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1995 English Publisher:Springer Science and Business Media LLCJournal:Foundations of Physics Letters, volume 8, pages 243-252 (issn: 0894-9875, eissn: 1572-9524,

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Authors: Stanley Gudder;

doi: 10.1007/bf02187348

Total extensions of effect algebras

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Abstract

It is shown that if the natural order on a total extension Open image in new window of an effect algebra Open image in new window coincides with the order on Open image in new window , then Open image in new window is unique. The structure of Open image in new window is called a QI-algebra. It is shown that a QI-algebra is less general than a QMV-algebra, but that a QI-algebra is equivalent to a quasi-linear QMV-algebra. Some examples are given and the properties of these structures are studied.

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