Modular median algebras
Modularity and distributivity of tolerance lattices of commutative inverse semigroups
Modyfications of Csákány's Theorem
Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.