  We extend the classical results on the symmetry inheritance of the canonical
electromagnetic fields, described by the Maxwell's Lagrangian, to a much wider
class of models, which include those of the Born-Infeld, power Maxwell and the
Euler-Heisenberg type. Symmetry inheriting fields allow the introduction of
electromagnetic scalar potentials and these are proven to be constant on the
Killing horizons. Finally, using the relations obtained along the analysis, we
generalize and simplify the recent proof for the symmetry inheritance of the
3-dimensional case, as well as give the first constraint for the higher
dimensional electromagnetic fields.
