  We study the singularity formation of strong solutions to the two-dimensional
(2D) Cauchy problem of the non-baratropic compressible magnetohydrodynamic
equations without heat conductivity. It is proved that the strong solution
exists globally if the density and the pressure are bounded from above. In
particular, the criterion is independent of the magnetic field and is just the
same as that of the compressible Navier-Stokes equations. Our method relies on
weighted energy estimates and a Hardy-type inequality.
