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Categorical Equivalence between $PMV_f$- product algebras and semi-low $f_u$-rings
- Publication Year :
- 2018
-
Abstract
- An explicit categorical equivalence is defined between a proper subvariety of the class of $PMV$-algebras, as defined by Di Nola and Dvure$\check{c}$enskij, to be called $PMV_f$-algebras, and the category of semi-low $f_u$-rings. This categorical representation is done using the prime spectrum of the $MV$-algebras, through the equivalence between $MV$-algebras and $l_u$-groups established by Mundici, from the perspective of the Dubuc-Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low $f_u$-rings associated to Boolean algebras are characterized. Besides we show that class of $PMV_f$-algebras is coextensive.
- Subjects :
- Mathematics - Logic
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1804.00565
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s11225-018-9832-6