International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 943565, 9 pages
doi:10.1155/2010/943565
𝒩-Structures Applied to Closed Ideals in BCH-Algebras
Young Bae Jun1
, Mehmet Ali Öztürk2
and Eun Hwan Roh3
1Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, South Korea
2Department of Mathematics, Faculty of Arts and Sciences, Adiyaman University, 02040 Adiyaman, Turkey
3Department of Mathematics Education (and IME), Chinju National University of Education, Chinju 660-756, South Korea
Abstract
The notions of 𝒩-subalgebras and 𝒩-closed ideals in BCH-algebras are introduced, and the relation between 𝒩-subalgebras and 𝒩-closed ideals is considered. Characterizations of 𝒩-subalgebras and 𝒩-closed ideals are provided. Using special subsets, 𝒩-subalgebras and 𝒩-closed ideals are constructed. A condition for an 𝒩-subalgebra to be an 𝒩-closed ideal is discussed. Given an 𝒩-structure, the greatest 𝒩-closed ideal which is contained in the 𝒩-structure is established.