Strictly join irreducible varieties of residuated lattices

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