So my understanding is that in ideal magnetohydrodynamics (MHD), we assume a conductivity of infinity, and that makes the electric field in a comoving frame equal to zero. As I was watching one derivation of the equations of ideal MHD, I also noticed that the conservative energy PDE was treated as adiabatic, e.g., excluding terms for heat transfer.
So my question is this: Is the adiabatic treatment of the fluid part of the assumptions of idealization of MHD? Or was this probably just a simplification of the individual deriving the equations? Are there any other assumptions we make for ideal MHD? Commenting on how good these (or any other) assumptions are would also be appreciated.