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Derivations on algebras of a non-commutative generalization of the Łukasiewicz logic. (English) Zbl 1380.06010

Summary: GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic semantics of the non-commutative Łukasiewicz infinite valued propositional fuzzy logic. In the paper, derivations on GMV-algebras (which are formally introduced in the same manner as derivations on rings) are investigated. A complete description of all derivations on any GMV-algebra is given.

MSC:

06D35 MV-algebras
03B52 Fuzzy logic; logic of vagueness
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