Copyright © 2012 Young Bae Jun and Sun Shin Ahn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling -ideals in -algebras is introduced, and related properties are investigated. Characterizations of a falling -ideal are established. Relations among falling -ideals, falling -ideals, falling -ideals, falling -subalgebras, and falling BCK-ideals are discussed.