State operators on GMV algebras

Abstract

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.