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For the magnetic greenhouse effect to operate, stars need to have magnetic fields with a longitudinal component $B\gtrsim 10^5 {\rm G}$ around the location of the H-burning shell. This is consistent with both a fossil field with surface amplitude $\sim 1 {\rm kG}$ on the main sequence, or a convective core dynamo generated field (equipartition strength $B \sim 10^5-10^6 {\rm G}$). The fraction of stars showing suppressed dipole modes in the data of \citet{Mosser_2011} is about 22\%, tentatively showing that red giants with magnetized cores are not just the descendants of Ap stars. A detailed analysis a large population of stars with suppressed dipole modes will put strong constraints on the amplitude and evolution of internal magnetic fields in stars of different mass (Stello et al. In prep.).  The asteroseismic technique described in this paper can be applied to stars burning He in their cores.Clump stars with strongly magnetized cores are also expected to show suppressed modes.  Observations of dipolar modes in He-burning clump  stars will put important constraints on the internal magnetic field of the immediate progenitors of white dwarfs. dwarfs (AuthorX et al. In prep.).