Quantale-valued sup-algebras

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Authors	ŠLESINGER Radek
Year of publication	2018
Type	Article in Periodical
Magazine / Source	Iranian Journal of Fuzzy Systems
MU Faculty or unit	Faculty of Science
Citation
Web	http://dx.doi.org/10.22111/ijfs.2017.3440
Doi	http://dx.doi.org/10.22111/IJFS.2018.3759
Field	General mathematics
Keywords	Q-order; Q-sup-lattice; Q-ordered algebra; Q-sup-algebra; quotient; subalgebra
Description	Based on the notion of Q-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of Q-sup-algebras - Q-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated by Zhang and Laan, we characterize their subalgebras and quotients, and following Solovyov, we show that the category of Q-sup-algebras is isomorphic to a certain subcategory of a category of Q-modules.
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