J. Neggers and H. S. Kim ([8]) introduced the notion of d-algebras which is another generalization of BC K -algebras. Y. B. Jun, E. H. Roh and H. S. Kim ([6]) introduced the notion of BH -algebra, which is a generalization
of BC H/BC I /BC K -algebras, i.e., (I); (II) and (IV) x ∗ y = 0 and y ∗ x = 0 imply x = y
for any x, y ∈ X .