English

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 (n+1)(n+1)-valued discrete state. We introduce nn-perfect pseudo-effect algebras as algebras which can be split into n+1n+1 comparable slices. We prove that the category of strong nn-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}
}