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2015 | OriginalPaper | Buchkapitel

9. How Do \(\ell \)-Groups and Po-Groups Appear in Algebraic and Quantum Structures?

verfasst von : Anatolij Dvurečenskij

Erschienen in: Petr Hájek on Mathematical Fuzzy Logic

Verlag: Springer International Publishing

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Abstract

In this survey we give an account of the relationships between \(\ell \)-groups and some important algebraic structures like MV-algebras, BL-algebras, and their non-commutative versions given by pseudo MV-algebras and pseudo BL-algebras. In a similar way we show how partially ordered groups are connected with quantum structures like orthomodular lattices, effect algebras and pseudo effect algebras. For the latter classes, an important role is played by various types of the Riesz Decomposition Property.

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Fußnoten
1
Notational convention: \(\odot \) binds stronger than \(\oplus \).
 
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Metadaten
Titel
How Do -Groups and Po-Groups Appear in Algebraic and Quantum Structures?
verfasst von
Anatolij Dvurečenskij
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-06233-4_9