As an hypothesis the sharp far–infrared turnovers in the spectra of several radio–quiet galactic nuclei [1–3] are attributed to the modifications of synchrotron emission arising from the presence of a thermal background plasma. We calculate the synchrotron emission from a power-law distribution of relativistic electrons N(γ) = Noγ–s in a large–scale random magnetic field of strength B embedded in a thermal plasma of density ne. Two major modifications of the classical vacuum theory of synchrotron emission are established [4]:

A) synchrotron sources can be optically thick only in a small frequency range around the Razin -Tsytovich frequency, whereas at smaller and higher frequencies the sources are optically thin;

B) at frequencies above VR the synchrotron intensity in a plasma behaves exactly the same way as in the vacuum case, whereas at frequencies below VR the intensity is exponentially reduced,