  The known Holstein-Primakoff and Dyson realizations of the Lie algebra
$sl(n+1), n=1,2,...$ in terms of Bose operators (Okubo S 1975 J. Math. Phys. 16
528) are generalized to the class of the quantum algebras $U_q[sl(n+1)]$ for
any $n$. It is shown how the elements of $U_q[sl(n+1)]$ can be expressed via
$n$ pairs of Bose creation and annihilation operators.
