International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 693090, 10 pages
Research Article

The Theory of Falling Shadows Applied to 𝑑 -Ideals in 𝑑 -Algebras

1Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Republic of Korea
2Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea

Received 24 August 2011; Accepted 9 December 2011

Academic Editor: Eun Hwan Roh

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 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.