  We study (strictly) join irreducible varieties in the lattice of subvarieties
of residuated lattices. We explore the connections with well-connected algebras
and suitable generalizations, focusing in particular on representable
varieties. Moreover we find weakened notions of Hallden completeness that
characterize join irreducibility. We characterize strictly join irreducible
varieties of basic hoops, and use the generalized rotation construction to find
strictly join irreducible varieties in subvarieties of MTL-algebras. We also
obtain some general results about linear varieties of residuated lattices, with
a particular focus on representable varieties, and a characterization for
linear varieties of basic hoops.
