This paper introduces various types of relative annihilator ideals, highlighting their relationships and implications.
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.
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Bordbar et al. (2025) studied this question.
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