Ideal theory of BE-algebras based on N-structures

Abstract

Using N-structures, the notion of an N-ideal in a BE-algebra is intro- duced. Characterizations of an N-ideal are discussed. Conditions for an N-structure to be an N-ideal are provided. To obtain a more gen- eral form of an N-ideal, a point N-structure which is (conditionally) employed in an N-structure is proposed. Using these notions, the con- cept of an ([e], [e]∨[c])-ideal is introduced, and related properties are investigated. Characterizations of ([e], [e]∨[c])-ideals are discussed.