Various Types of Relative Annihilator Ideals in a BCK-Algebra

In this paper, we introduce various types of relative annihilator ideals and explore the relationships between them. We establish the necessary conditions for a subset to qualify as an [Formula: see text]-relative, [Formula: see text]-relative, [Formula: see text]-relative, [Formula: see text]-relative, or [Formula: see text]-relative annihilator ideal. Additionally, we demonstrate how an [Formula: see text]-relative (respectively, [Formula: see text]-relative, [Formula: see text]-relative, [Formula: see text]-relative, or [Formula: see text]-relative) annihilator ideal can be constructed from a given subset or positive implicative ideal. Finally, we investigate the behavior of these annihilator ideals under homomorphisms, examining both their homomorphic images and preimages.