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arXiv · 1203.0988

Discrete $(n+1)$-valued states and $n$-perfect pseudo-effect algebras

Anatolij Dvurecenskij·Yongjian Xie·Aili Yang
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Abstract

We give sufficient and necessary conditions to guarantee that a pseudo-effect algebra admits an $(n+1)$-valued discrete state. We introduce $n$-perfect pseudo-effect algebras as algebras which can be split into $n+1$ comparable slices. We prove that the category of strong $n$-perfect pseudo-effect algebras is categorically equivalent to the category of torsion-free directed partially ordered groups of a special type.

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Anatolij Dvurecenskij, Yongjian Xie, Aili Yang. 2012-03-01. Discrete $(n+1)$-valued states and $n$-perfect pseudo-effect algebras. https://arxiv.org/abs/1203.0988

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