When the lexicographic product of two po-groups has the Riesz decomposition property

When the lexicographic product of two po-groups has the Riesz decomposition property 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 $${{\rm RDP}_1}$$ RDP 1 , a stronger type of RDP. We recall that a very strong type of RDP, $${{\rm RDP}_2}$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png algebra universalis Springer Journals

When the lexicographic product of two po-groups has the Riesz decomposition property

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Springer International Publishing
Copyright © 2017 by Springer International Publishing
Mathematics; Algebra
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