How Do $$\ell $$-Groups and Po-Groups Appear in Algebraic and Quantum Structures?

Dvurečenskij, Anatolij

doi:10.1007/978-3-319-06233-4_9

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2015

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“…This result was extended for pseudo MV-algebras, a non-commutative generalization of MV-algebras in the sense of [GeIo, Rac], in [Dvu1], where a categorical equivalence of the category of pseudo MV-algebras and the category of unital ℓ-groups (not necessarily Abelian) was established. More about a relation between other algebraic structures like BL-algebras or pseudo BLalgebras and ℓ-groups was presented in [Dvu3].…”

Section: Introductionmentioning

confidence: 99%

Riesz decomposition properties and the lexicographic product of po-groups

Dvurečenskij

2015

Soft Comput

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Abstract. We establish conditions when a certain type of the Riesz Decomposition Property (RDP) holds in the lexicographic product of two po-groups. It is well known that the resulting product is an ℓ-group if and only if the first one is linearly ordered and the second one is an ℓ-group. This can be equivalently studied as po-groups with a special type of the RDP. In the paper we study three different types of RDP's. RDP's of the lexicographic products are important for the study of 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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Section: Introductionmentioning

confidence: 99%