Two notions of MV-algebraic semisimplicity relative to fixed MV-chains

Abstract

We initiate a study of two general concepts of semisimplicity for MV-algebras by replacing the standard MV-algebra with an arbitrary MV-chain . These generalised notions are called -semisimple MV-algebras and -semisimple MV-algebras. We obtain several of their characterisations and explore in more-depth the case of perfect MV-chains.