MV-algebras with operators (the commutative and the non-commutative case)

In the present paper we define the (pseudo) MV-algebras with n-ary operators, generalizing MV-modules and product MV-algebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MV-algebra and the operators defined on the corresponding ℓ-group....

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Bibliographic Details
Published inDiscrete mathematics Vol. 274; no. 1; pp. 41 - 76
Main Authors Flondor, Paul, Leuştean, Ioana
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 06.01.2004
Elsevier
Subjects
Combinatorics. Ordered structures
Exact sciences and technology
Mathematics
MV-algebra
Operator
Order, lattices, ordered algebraic structures
Pseudo MV-algebra
Sciences and techniques of general use
ℓ u-group
06F20
Operator
06D30
Pseudo MV-algebra
ℓ u-group
MV-algebra
Distributive lattice
Algebra
Network
Module
lu group
MV algebra
Axiomatic
Operator theory
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Summary:In the present paper we define the (pseudo) MV-algebras with n-ary operators, generalizing MV-modules and product MV-algebras. Our main results assert that there are bijective correspondences between the operators defined on a pseudo MV-algebra and the operators defined on the corresponding ℓ-group. We also provide a categorical framework and we prove the analogue of Mundici's categorical equivalence between MV-algebras and abelian ℓ-groups with strong unit. Thus, the category of pseudo MV-algebras with operators is equivalent to some category of ℓ-groups with operators.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(03)00080-3