(Fuzzy)‎ Ideals of BN-Algebras

الملخص EN

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 fuzzyset 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.