  We study the two-dimensional generalized magnetohydrodynamics system with
generalized dissipation and diffusion in terms of fractional Laplacians. It is
known that the classical magnetohydrodynamics system with full Laplacians in
both dissipation and diffusion terms admits a unique global strong solution
pair. Making use of the special structure of the system in the two-dimensional
case, we show in particular that the solution pair remains smooth when we have
zero dissipation but only magnetic diffusion with its power of the fractional
Laplacian $\beta > \frac{3}{2}$.
