Abstract
We study conditions when a certain type of the Riesz Decomposition Property (RDP for short) holds in the lexicographic product of two po-groups. Defining two important properties of po-groups, we extend known situations showing that the lexicographic product satisfies RDP or even \({{\rm RDP}_1}\), a stronger type of RDP. We recall that a very strong type of RDP, \({{\rm RDP}_2}\), entails that the group is lattice ordered. RDP's of the lexicographic products are important for the study of lexicographic pseudo effect algebras, or perfect types of pseudo MV-algebras and pseudo effect algebras, where infinitesimal elements play an important role both for algebras as well as for the first order logic of valid but not provable formulas.
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Presented by S. Pulmannova.
This work was supported by the grant VEGA No. 2/0069/16 SAV, and GAČR 15-15286S.
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Dvurečenskij, A., Zahiri, O. When the lexicographic product of two po-groups has the Riesz decomposition property. Algebra Univers. 78, 67–91 (2017). https://doi.org/10.1007/s00012-017-0447-y
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DOI: https://doi.org/10.1007/s00012-017-0447-y