A Hopf algebra isomorphism between two realizations of the quantum affine algebra U_q(widehat{gl(2)})

We consider the algebra isomorphism found by Frenkel and Ding between the RLL and the Drinfeld realizations of $U_q(\widehat{gl(2)})$. After we note that this is not a Hopf algebra isomorphism, we prove that there is a unique Hopf algebra structure for the Drinfeld realization so that this isomorphism becomes a Hopf algebra isomorphism. Though more complicated, this Hopf algebra structure is also closed, just as the one found previously by Drinfeld.