Generalized co-annihilator of BL-algebras

In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of co-annihilator and the set of the form x(-1) F where F is a filter, and study basic properties of generalized co-annihilators. We also introduce the notion of involutory filters relative to a filter F and prove that the set of all involutory filters relative to a filter with respect to the suit operations is a complete Boolean lattice and BL-algebra. We use the technology of generalized co-annihilators to give characterizations of prime filters and minimal prime filters, respectively. In particular, we give a representation of co-annihilators in the quotient algebra of a BL-algebra L via a filter F by means of generalized co-annihilators relative to F in L: