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2015 | OriginalPaper | Chapter

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

Author : Anatolij Dvurečenskij

Published in: Petr Hájek on Mathematical Fuzzy Logic

Publisher: 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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previous chapter Two Principles in Many-Valued Logic
next chapter Semi-linear Varieties of Lattice-Ordered Algebras
Footnotes
1
Notational convention: \(\odot \) binds stronger than \(\oplus \).
 
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Metadata
Title
How Do -Groups and Po-Groups Appear in Algebraic and Quantum Structures?
Author
Anatolij Dvurečenskij
Copyright Year
2015
Book
Petr Hájek on Mathematical Fuzzy Logic

Print ISBN: 978-3-319-06232-7

Electronic ISBN: 978-3-319-06233-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-06233-4_9

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