Quantum Z-algebras and representations of quantum affine algebras

Generalizing our earlier work, we introduce the homogeneous quantum $Z$-algebras for all quantum affine algebras $\text{alg}$ of type one. With the new algebras we unite previously scattered realizations of quantum affine algebras in various cases. As a result we find a realization of $U_q(F_4^{(1)})$.