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arXiv · 1006.2795

Type-Decomposition of a Pseudo-Effect Algebra

David Foulis·Sylvia Pulmannová·Elena Vincekova
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Abstract

The theory of direct decomposition of a centrally orthocomplete effect algebra into direct summands of various types utilizes the notion of a type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly) noncommutative version of an effect algebra. In this article we develop the basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set to PEAs, and show that TD sets induce decompositions of centrally orthocomplete PEAs into direct summands.

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David Foulis, Sylvia Pulmannová, Elena Vincekova. 2010-06-10. Type-Decomposition of a Pseudo-Effect Algebra. https://doi.org/10.1007/s10701-009-9344-3

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