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 Dvure?enskij 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.
state state-morphism state \(gmv\) algebra \(gmv\) algebra state-morphism \(gmv\) algebra \(mv\)algebra