Falling ð ‘‘ -Ideals in ð ‘‘ -Algebras

Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in ð ‘‘ -algebras is established. The notions of a falling ð ‘‘ -subalgebra, a falling ð ‘‘ -ideal, a falling ð µ ð ¶ ð ¾ -ideal, and a falling ð ‘‘ ♯ -ideal of a ð ‘‘ -algebra are introduced. Some fundamental properties are investigated. Relations among a falling ð ‘‘ -subalgebra, a falling ð ‘‘ -ideal, a falling ð µ ð ¶ ð ¾ -ideal, and a falling ð ‘‘ ♯ -ideal are stated. Characterizations of falling ð ‘‘ -ideals and falling ð ‘‘ ♯ -ideals are discussed. A relation between a fuzzy ð ‘‘ -subalgebra and a falling ð ‘‘ -subalgebra is provided.