Discrete $(n+1)$-valued states and $n$-perfect pseudo-effect algebras
Rings and Algebras
2012-03-06 v1
Abstract
We give sufficient and necessary conditions to guarantee that a pseudo-effect algebra admits an -valued discrete state. We introduce -perfect pseudo-effect algebras as algebras which can be split into comparable slices. We prove that the category of strong -perfect pseudo-effect algebras is categorically equivalent to the category of torsion-free directed partially ordered groups of a special type.
Keywords
Cite
@article{arxiv.1203.0988,
title = {Discrete $(n+1)$-valued states and $n$-perfect pseudo-effect algebras},
author = {Anatolij Dvurecenskij and Yongjian Xie and Aili Yang},
journal= {arXiv preprint arXiv:1203.0988},
year = {2012}
}