A new ordering relation on lattices applied to weak congruences
Vera Lazarević, Andreja Tepavčević · 2001
Starting from an arbitrary codistributive element a in an algebraic lattice L, a new operation ⁄a on the underlying set L is defined. This operation determines an ordering relation on L. A properties of the new poset are investigated. Some necessary and some sucient conditions under which it is a lattice are presented 1 . An application of the results to the weak congruence lattice is given. A new characterization of the Congruence Extension Property (CEP) in terms of weak congruences under the new ordering is obtained.