Varieties having directly decomposable congruence classes
Varieties having distributive lattices of quasiorders
Varieties having the congruence extension property
Varieties of algebras with equationally definable zeros
Varieties of groupoids determined by short linear identities
Varieties of -groups are torsion classes
Varieties of universal algebras with normal local projections.
Varieties satisfying the triangular scheme need not be congruence distributive
A diagrammatic scheme characterizing congruence distributivity of congruence permutable algebras was introduced by the first author in 2001. It is known under the name Triangular Scheme. It is known that every congruence distributive algebra satisfies this scheme and an algebra satisfying the Triangular Scheme which is not congruence distributive was found by E. K. Horváth, G. Czédli and the autor in 2003. On the other hand, it was an open problem if a variety of algebras satisfying the Triangular...
Varieties which are locally regular and permutable at 0
Varieties with rectangular ideals