Falling Pseudo d-Ideals and d-Subalgebras in Pseudo d-Algebras

Based on the theory of a falling shadow which was first formulated by Wang [15], a theoretical approach of the pseudo ideal structure in pseudo d-algebras is established. Several properties are investigated, and relations among a falling pseudo d-subalgebra, a falling pseudo BCK-ideal and a falling pseudo d-ideal are discussed. A characterization of a falling pseudo d-ideal is provided. Conditions for a falling shadow to be a falling pseudo BCK-ideal, and for a falling pseudo BCK-ideal to be a falling pseudo d-ideal are considered.