Abstract
Fraser and Horn, and independently Hu, studied varieties of algebras satisfying the property that for every
every congruence
is a product congruence, i.e.,
for some
i = 1, 2. Varieties of rings with identity and congruence distributive varieties of algebras satisfy this property. It is easy to show that an algebra
has the Fraser–Horn–Hu property if and only if the map
is a lattice isomorphism from
to
The property was later referred to in the literature as the Fraser–Horn–Hu property. It turns out that the Fraser–Horn–Hu property is a Mal’cev condition for varieties. In this paper, we generalize this property to varieties of ordered algebras. The classic result of Fraser, Horn and Hu follows as a special case.