principal ideal Principal Ideals in the Congruence Semilattice of a Path Authors: Fomina E. O. It is proven that principal ideals generated by congruences of a path having the same type are isomorphic lattices. The number of elements, atoms and coatoms is found for the principal ideal generated by a given congruence of a path. Read more about Principal Ideals in the Congruence Semilattice of a Path