Monadic GMV-algebras

Monadic MV –algebras are an algebraic model of the predicate calculus of the Lukasiewicz infinite valued logic in which only a single individual variable occurs. GMV -algebras are a non-commutative generalization of MV -algebras and are an algebraic counterpart of the non-commutative Lukasiewicz infinite valued logic. We introduce monadic GMV -algebras and describe their connections to certain couples of GMV -algebras and to left adjoint mappings of canonical embeddings of GMV algebras. Furthermore, functional MGMV -algebras are studied and polyadic GMV algebras are introduced and discussed.