Congruences and d-filters of principal p-algebras

AbstractThe concept of d-filters is introduced in p-algebras. Some properties of d-filters are studied. It is proved that the class Fd(L) of all d-filters of a p-algebra L is a bounded complete lattice. A characterization of d-filters of a principal p-algebra is given. Also many properties of congruences induced by the d-filters are derived. A relationship between the d-filters of a principal p-algebra L and the congruences in [Φ, ∇] is established