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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 516418, 14 pages
Research Article

Falling 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
3Department of Mathematics Education, Hannam University, Daejeon 306-791, Republic of Korea

Received 24 August 2011; Accepted 25 October 2011

Academic Editor: Bo Yang

Copyright © 2011 Young Bae Jun et al. 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.


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 𝐡 𝐢 𝐾 -ideal, and a falling 𝑑 β™― -ideal of a 𝑑 -algebra are introduced. Some fundamental properties are investigated. Relations among a falling 𝑑 -subalgebra, a falling 𝑑 -ideal, a falling 𝐡 𝐢 𝐾 -ideal, and a falling 𝑑 β™― -ideal are stated. Characterizations of falling 𝑑 -ideals and falling 𝑑 β™― -ideals are discussed. A relation between a fuzzy 𝑑 -subalgebra and a falling 𝑑 -subalgebra is provided.