International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 943565, 9 pages
doi:10.1155/2010/943565
Research Article

𝒩-Structures Applied to Closed Ideals in BCH-Algebras

Young Bae Jun,1 Mehmet Ali Öztürk,2 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

Received 28 December 2009; Revised 2 February 2010; Accepted 9 February 2010

Academic Editor: Ilya M. Spitkovsky

Copyright © 2010 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.

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.