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The Scientific World Journal
Volume 2015, Article ID 925040, 9 pages
http://dx.doi.org/10.1155/2015/925040
Research Article

(Fuzzy) Ideals of BN-Algebras

1Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1H, 20-708 Lublin, Poland
2Institute of Mathematics and Physics, Siedlce University, 3 Maja 54, 08-110 Siedlce, Poland

Received 16 September 2014; Revised 17 December 2014; Accepted 28 December 2014

Academic Editor: Arsham B. Saeid

Copyright © 2015 Grzegorz Dymek and Andrzej Walendziak. 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 an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained.