Annihilators in BCK-Algebras
Radomír Halaš · Czechoslovak Mathematical Journal · 2003
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 $${\mathcal{D}\left( \mathcal{A} \right)}$$ .