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arXiv · 1211.2464

The lexicographic product of po-groups and $n$-perfect pseudo effect algebras

A. Dvurečenskij·J. Krňávek
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Abstract

We will study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. A special attention will be paid to the lexicographic product of the group of the integers with an arbitrary po-group. Then we apply these results to the study of $n$-perfect pseudo effect algebras. We show that the category of strong $n$-perfect pseudo-effect algebras is categorically equivalent to the category of torsion-free directed partially ordered groups with RDP$_1.$

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A. Dvurečenskij, J. Krňávek. 2012-11-11. The lexicographic product of po-groups and $n$-perfect pseudo effect algebras. https://doi.org/10.1007/s10773-013-1568-5

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