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The Lexicographic Product of Po-groups and n-Perfect Pseudo Effect Algebras

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Abstract

We study the existence of different types of the Riesz Decomposition Property for the lexicographic product of two partially ordered groups. Special attention is paid to the lexicographic product of the group of 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 RDP1.

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Acknowledgement

The authors are very indebted to anonymous referees for their careful reading and suggestions which helped us to improve the readability of the paper.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

  2. Depart. Algebra Geom., Palacký Univer., 17. listopadu, 771 46, Olomouc, Czech Republic

    Anatolij Dvurečenskij & Jan Krňávek

Authors
  1. Anatolij Dvurečenskij
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  2. Jan Krňávek
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Correspondence to Anatolij Dvurečenskij.

Additional information

The paper has been supported by Center of Excellence SAS—Quantum Technologies—, ERDF OP R&D Project meta-QUTE ITMS 26240120022, Slovak Research and Development Agency under the contract APVV-0178-11, the grant VEGA No. 2/0059/12 SAV and by CZ.1.07/2.3.00/20.0051.

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Dvurečenskij, A., Krňávek, J. The Lexicographic Product of Po-groups and n-Perfect Pseudo Effect Algebras. Int J Theor Phys 52, 2760–2772 (2013). https://doi.org/10.1007/s10773-013-1568-5

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  • DOI: https://doi.org/10.1007/s10773-013-1568-5

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