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%Internal stellar magnetic fields are inaccessible to direct observations and little is known about their amplitude, geometry and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars will suppress dipole oscillation modes. This arises from a magnetic greenhouse effect trapping oscillation mode energy within the core. Suppressed dipole modes are indeed observed in a substantial fraction of red giants observed by \textit{Kepler}, and we interpret these as stars with magnetized cores. %We find field strengths larger than roughly $10^5 \,{\rm G}$ can account for the observed suppression, and in one case measure a core field strength of $\sim 10^7 \,{\rm G}$, indicating many red giants have retained fossil fields or previously hosted a powerful core dynamo.  Internal stellar magnetic fields are inaccessible to direct observations and little is known about their amplitude, geometry and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars will suppress dipole oscillation modes. This arises from a magnetic greenhouse effect trapping oscillation mode energy within the core. \textit{Kepler} asteroseismology finds many red giants with suppressed dipole modes that we interpret as stars with strongly  magnetized cores. We find field strengths larger than roughly $10^5 \,{\rm G}$ can account for the observed suppression, and in one case measure a core field strength of $\sim 10^7 \,{\rm G}$, indicating many red giants have retained fossil fields or previously hosted a powerful core dynamo.