Y. Imai and K. Iséki introduced two classes of abstract algebras: BCK-
algebras and BCI-algebras ([2, 3]). It is known that the class of BCK-
algebras is a proper subclass of the class of BCI-algebras. In [4, 5] Q. P.
Hu and X. Li introduced a wide class of abstract algebras: BCH-algebras.
They have shown that the class of BCI-algebras is a proper subclass of
the class of BCH-algebras. J. Neggers and H. S. Kim introduced in [8]
the notion of d-algebras, i.e. algebras satisfying (1) xx = 0, (5) 0x = 0,
(6) xy = 0 and yx = 0 imply x = y, which is another useful generalization
of BCK-algebras,