The theory of falling shadows applied to d-ideals in d-algebras

On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling d ^*-ideals in d -algebras is introduced, and related properties are investigated. Characterizations of a falling d ^*-ideal are established. Relations among falling d -ideals, falling d ^*-ideals, falling d ^*-ideals, falling d ^*-subalgebras, and falling BCK-ideals are discussed.