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Lexicographic product vs \(\mathbb Q\)-perfect and \(\mathbb H\)-perfect pseudo effect algebras

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Abstract

We study the Riesz decomposition property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed into a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.

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Acknowledgments

The authors are very indebted to anonymous referees for their careful reading and suggestions which helped to improve the readability of the paper. The paper has been supported by the 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 and CZ.1.07/2.3.00/20.0060.

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Correspondence to Anatolij Dvurečenskij.

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Communicated by L. Spada.

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Dvurečenskij, A., Kolařík, M. Lexicographic product vs \(\mathbb Q\)-perfect and \(\mathbb H\)-perfect pseudo effect algebras. Soft Comput 18, 1041–1053 (2014). https://doi.org/10.1007/s00500-014-1228-6

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