The present paper is concerned with dynamical processes in an electrically conducting rotating incompressible liquid with consideration of the inhomogeneity of density and the magnetic field diffusion effect. By introducing auxiliary functions, the given system of partial differential equations can be reduced to one scalar equation. This in turn suggests the analytic nature of the magnetohydrodynamic characteristics under consideration. In this study, the dissipative effects (the magnetic field diffusion) are taken into account.