Representation by triples of algebras with an MV-retract

We introduce the notion of generalized rotation of a residuated lattice and characterize the varieties of bounded residuated lattices they generate, which we name MVRn. These algebras have a retraction onto a hyperarchimedean MV-algebra. Then we characterize algebras in MVRn as triples made of an MV...

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Bibliographic Details
Published in:Fuzzy sets and systems 2019-08, Vol.369, p.82-102
Main Authors: Busaniche, Manuela, Marcos, Miguel Andrés, Ugolini, Sara
Format: Article
Language:English
Subjects:
Categorical equivalence
Residuated lattices
Rotation
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Summary:We introduce the notion of generalized rotation of a residuated lattice and characterize the varieties of bounded residuated lattices they generate, which we name MVRn. These algebras have a retraction onto a hyperarchimedean MV-algebra. Then we characterize algebras in MVRn as triples made of an MV-algebra, a residuated lattice with a nucleus, and an operator joining them.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2018.10.024