Orthocomplete Pseudo MV-algebras

2015/05/16 by Dvurečenskij, Anatolij, Zahiri, Omid
#06D35 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1505.04304

Abstract

Pseudo MV-algebras are a non-commutative generalization of MV-algebras. The main purpose of the paper is to introduce and investigate orthocomplete pseudo MV-algebras. We use the concepts of projectable pseudo MV-algebras and large pseudo MV-subalgebras to introduce orthocomplete pseudo MV-algebras. Then we apply a generalization of the Mundici's functor to an orthocompletion of an representable ℓ-group to prove that each representable pseudo MV-algebra has an orthocompletion. In particular, our results are valid also for MV-algebras.

Related

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• Some results on pseudo MV-algebras with square roots
• Representation and Embedding of Pseudo MV-algebras with Square Roots II. Closures
• Representation and Embedding of Pseudo MV-algebras with Square Roots I. Strict Square Roots
• Mv-algebras And Partially Cyclically Ordered Groups