Orthocomplete pseudo MV-algebras

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....

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Bibliographic Details
Published inInternational journal of general systems Vol. 45; no. 7-8; pp. 889 - 909
Main Authors Dvurečenskij, A., Zahiri, O.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 16.11.2016
Taylor & Francis LLC
Subjects
Algebra
Boolean element
essential extension
group
orthocompletion
projectable pseudo MV-algebra
Pseudo MV-algebra
unital
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Summary: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 functor to an orthocompletion of an representable -group to prove that each representable pseudo MV-algebra has an orthocompletion. In particular, our results are valid also for MV-algebras.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0308-1079
1563-5104
DOI:10.1080/03081079.2016.1220008