  We study the two-dimensional generalized magnetohydrodynamics-$\alpha$ system
with fractional Laplacians in the dissipative and diffusive terms. We show that
the solution pair of velocity and magnetic fields preserves their initial
regularity in all cases when the powers add up to one. This settles the global
regularity issue in the general case which was remarked by the authors in [33]
to be a problem.
