Varieties of BL-algebras I: general properties

The aim of this paper is to lay down some facts and techniques that are useful in order to describe the lattice of subvarieties of BL-algebras. The results include: a representation of linearly ordered BL-algebras as ordinal sums of linearly ordered Wajsberg hoops; a description of subalgebras and homomorphic images of totally ordered BL-algebras in terms of ordinal sums; a characterization of generic BL-algebras, i.e. the totally ordered BL-algebras that generate the whole variety; a full description of the subdirectly irreducible members of the variety generated by ordinal sums of finitely many Wajsberg hoops.