State operators on GMV algebras

Flaminio and Montagna recently introduced state $$MV$$ algebras as $$MV$$ algebras with an internal state in the form of a unary operation. Di Nola and Dvurečenskij further presented a stronger variation of state $$MV$$ algebras called state-morphism $$MV$$ algebras. In the paper we present state $$GMV$$ algebras and state-morphism $$GMV$$ algebras which are non-commutative generalizations of the mentioned algebras.

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