State morphism MV-algebras

We present a complete characterization of subdirectly irreducible MV-algebras with internal states (SMV-algebras). This allows us to classify subdirectly irreducible state morphism MV-algebras (SMMV-algebras) and describe single generators of the variety of SMMV-algebras, and show that we have a continuum of varieties of SMMV-algebras.

► A complete characterization of subdirectly irreducible state MV-algebras.
► The number of the varieties of SMMV-algebras is uncountable.
► Equational basis for the varieties of representable and local SMMV-algebras.
► A subdirectly irreducible SMMV-algebra can be embedded into a diagonal one.
► A description of generators of varieties of SMMV-algebras.