On Generalized Annihilators in BL-Algebras

The theory of generalized annihilators on BL-algebras are developed in this paper. Firstly, some properties of generalized annihilators on BL-algebras are supplemented. Secondly, we introduce the notion of involutory ideals relative to an ideal I and denote the set of all of them by \(S_{I}(L)\). Then \(S_{I}(L)\) can be made into a complete Boolean lattice and a BL-algebra with respect to the suit operations, respectively. Finally, the prime ideals can be characterized by the generalized annihilators, and the generalized annihilators of the quotient algebra induced by an ideal I in a BL-algebra L are studied.