Y. Imai and K. Is´eki introduced two classes of abstract algebras: BCK-algebras
and BCI-algebras([3, 4]). It is known that the class of BCK-algebras is a proper
subclass of the class of BCI-algebras. In [1, 2], Q. P. Hu and X. Li introduced a
wide class of abstracts: BCH-algebras. They have shown that the class of BCIalgebras
is a proper subclass of the class of BCH-algebras. In [5], J. Neggers,
etc introduced the notion of an Q-algebra as a dualization of a generation
of a BCK/BCI-algebras. In this paper, the concept of a right fixed map in
an Q-algebra is discussed and some fundamental properties to Q-algebras are
discussed.