d-ideals and injective ideals in a distributive lattice

The concepts of d-ideals and injective ideals are introduced in a distributive lattice with respect to derivations. d-ideals are characterized in terms of principal ideals of a distributive lattice. Further, an equivalent condition is derived for a d-ideal to become an injective ideal. Also the Stone’s theorem for ideals of a distributive lattice is extended to the case of injective ideals.