Relative co-annihilators in lattice equality algebras

We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among $ \vee$-irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra $ \mathcal{\mathbb{E}} $ and $ \mathbb{F} $ a filter of $ \mathcal{\mathbb{E}} $, we define the set of all $ \mathbb{F} $-involutive filters of $ \mathcal{\mathbb{E}} $ and show that by defining some operations on it, it makes a BL-algebra.