Analysis; Algebra and Number Theory; Numerical Analysis; Discrete Mathematics and Combinatorics; Control and Optimization
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Abstract:
An axiomatization of classical propositional logic is provided by means of Boolean
algebras which are term equivalent to Boolean rings. This is important because rings form a
classical part of algebra whose tools can be used for the investigations. The Łukasiewicz many-
valued logic was axiomatized via so-called MV-algebras by C. C. Chang in 1950’s. MV-algebras
are successfully applied in the logic of quantum mechanics and hence they are considered as
quantum structures. It is a natural question if also MV-algebras have their alter ego among
classical structures. For this reason the so-called Łukasiewicz semirings were introduced by
the first author and his collaborators in [3] – [4]. As shown, Łukasiewicz semirings are term
equivalent to MV-algebras and we can use with advantage several developed tools for their study.
In particular, we investigate derivations in semirings which were introduced formerly but here
these semirings are enriched by an involution.
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Research Areas:
außerhalb der gesamtuniversitären Forschungsschwerpunkte: 100%