Subvarieties of BL-algebras generated by single-component chains (Q1407568)

In this paper we study and equationally characterize the subvarieties of \textbf{BL}, the variety of BL-algebras, which are generated by families of single-component BL-chains, i.e. MV-chains, product-chains or Gödel-chains. Moreover, it is proved that they form a segment of the lattice of subvarieties of \textbf{BL} which is bounded by the Boolean variety and the variety generated by all single-component chains, called \textbf{Ł}\(\mathbf{\Pi}\)\textbf{G}. Finally, we prove that all their corresponding logics are semi-standard complete.