The congruence lattice 
of a universal algebra 
is the lattice
of all algebra congruences on 
, ordered by inclusion. The meet is
the intersection of two relations.
The join is the smallest algebra
congruence containing both relations (Burris and
Sankappanavar 1981, pp. 35-37).
The least element is the equality relation, and the greatest is 
.
If 
is finite, its congruence lattice is finite.
For example, the congruence lattice of the ring 
is a three-element chain, corresponding
to its ideals 
, 
, and 
.
The finite lattice representation problem asks whether every finite lattice arises as the full congruence lattice of a finite universal algebra.
