On some extensions of the class of MV-algebras

Abstract

In the present paper we will ask for the lattice L(MV Ex ) of subvarieties of the variety defined by the set Ex(MV) of all externally compatible identities valid in the variety MV of all MV-algebras. In particular, we will find all subdirectly irreducible algebras from the classes in the lattice L(MV Ex ) and give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of MV-algebras.