Type-Decomposition of a Pseudo-Effect Algebra

Details Type-Decomposition of a Pseudo-Effect Algebra Type-Decomposition of a Pseudo-Effect Algebra

2010-06-10

arxiv.org/abs/1006.2795v1

Mathematics

Rings and Algebras

18 pages

Scientific paper

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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