Dimension theory for generalized effect algebras
Mathematical Physics
2012-06-15 v1 math.MP
Abstract
In this paper we define and study dimension generalized effect algebras (DGEAs), i.e., Dedekind orthocomplete and centrally orthocomplete generalized effect algebras equipped with a dimension equivalence relation. Our theory is a bona fide generalization of the theory of dimension effect algebras (DEAs), i.e., it is formulated so that, if a DGEA happens to be an effect algebra (i.e., it has a unit element), then it is a DEA. We prove that a DGEA decomposes into type I, II, and III DGEAS in a manner analogous to the type I/II/III decomposition of a DEA.
Cite
@article{arxiv.1206.3052,
title = {Dimension theory for generalized effect algebras},
author = {David J. Foulis and Sylvia Pulmannova},
journal= {arXiv preprint arXiv:1206.3052},
year = {2012}
}