Erratum to “State-morphism MV-algebras” [Ann. Pure Appl. Logic 161 (2009) 161–173]

Recently, the first two authors characterized in Di Nola and Dvurečenskij (2009) [1] subdirectly irreducible state-morphism MV-algebras. Unfortunately, the main theorem (Theorem 5.4(ii)) has a gap in the proof of Claim 10, as the example below shows. We now present a correct characterization and its correct proof.