Falling d-ideals in d-algebras

Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in d-algebras is established. The notions of a falling d-subalgebra, a falling d-ideal, a falling BCK-ideal, and a falling d ^#-ideal of a d-algebra are introduced. Some fundamental properties are investigated. Relations among a falling d-subalgebra, a falling d-ideal, a falling BCK-ideal, and a falling d ^#-ideal are stated. Characterizations of falling d-ideals and falling d ^#-ideals are discussed. A relation between a fuzzy d-subalgebra and a falling d-subalgebra is provided.