Relative Annihilators in BCI-algebras

‎In this paper‎, ‎for any two subsets A and C of a BCI-algebra X, ‎the concept of relative annihilator of A with respect to C‎, ‎denoted by (C:A)‎, ‎is introduced and some related properties are investigated‎. ‎Using this concept‎, ‎some necessary and sufficient conditions for a BCI-algebra to be p-semisimple is established‎. ‎Moreover‎, ‎for any normal ideal A and ideal C of a BCI-algebra X‎, ‎it is proved that (C:A) is the relative pseudocomplement of A with respect to C‎. ‎Finally‎, ‎applying the concept of relative annihilator‎, ‎the involutory ideal with respect to an ideal is defined and it is shown that the set of all involutory ideals with respect to a normal ideal forms a complete and complemented lattice