title: (Fuzzy) Ideals of BN-Algebras.
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.
authors.affiliation: Institute of Mathematics and Computer Science, The John Paul II Catholic University of Lublin, Konstantynów 1H, 20-708 Lublin, Poland.
authors.forename: Grzegorz
authors.identifier: 0000-0002-6540-997X
authors.initials: G
authors.lastname: Dymek
authors.affiliation: Institute of Mathematics and Physics, Siedlce University, 3 Maja 54, 08-110 Siedlce, Poland.
authors.forename: Andrzej
authors.initials: A
authors.lastname: Walendziak