Annihilators in BCK-Algebras

We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra $\mathcal{A}$ . We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice ${\mathcal{D}\left( \mathcal{A} \right)}$ of all deductive systems on $\mathcal{A}$ . Moreover, relative annihilators of ${C \in \mathcal{D}\left( \mathcal{A} \right)}$ with respect to ${B{\text{in}}\mathcal{D}\left( \mathcal{A} \right)}$ are introduced and serve as relative pseudocomplements of C w.r.t. B in ${\mathcal{D}\left( \mathcal{A} \right)}$ .