Derivations on algebras of a non-commutative generalization of the Łukasiewicz logic

Abstract

GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic semantics of the non-commutative Lukasiewicz 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.