Various Types of Relative Annihilator Ideals in a BCK-Algebra

Abstract

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 S-relative, I-relative, PI-relative, c-relative, or Im-relative annihilator ideal. Additionally, we demonstrate how an S-relative (respectively, I-relative, PI-relative, c-relative, or Im-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.