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We present high angular resolution (~2 mas) radio continuum observations offive Seyfert galaxies with flat-spectrum radio nuclei, using the VLBA at 8.4GHz. The goal of the project is to test whether these flat-spectrum coresrepresent thermal emission from the accretion disk, as inferred previously byGallimore et al. for NGC 1068, or non-thermal, synchrotron self-absorbedemission, which is believed to be responsible for more powerful, flat-spectrumnuclear sources in radio galaxies and quasars. In four sources (T0109-383, NGC2110, NGC 5252, Mrk 926), the nuclear source is detected but unresolved by theVLBA, indicating brightness temperatures in excess of 10^8 K and sizes, onaverage, less than 1 pc. We argue that the radio emission is non-thermal andsynchrotron self-absorbed in these galaxies, but Doppler boosting byrelativistic outflows is not required. Synchrotron self-absorption brightnesstemperatures suggest intrinsic source sizes smaller than ~0.05-0.2 pc, forthese four galaxies, the smallest of which corresponds to a light-crossing timeof ~60 light days or 10^4 gravitational radii for a 10^8 M_sun black hole.  We also present MERLIN and VLA observations of NGC 4388, which was undetectedby the VLBA, and argue that the observed, flat-spectrum, nuclear radio emissionin this galaxy represents optically thin, free-free radiation from densethermal gas on scales ~0.4 to a few pc. It is notable that the two Seyfertgalaxies with detected thermal nuclear radio emission (NGC 1068 and NGC 4388)both have large X-ray absorbing columns, suggesting that columns in excess of\~10^{24} cm^{-2} are needed for such disks to be detectable. (Abridged)Comment: 36 pages including 5 tables and 4 figures; accepted for publication  in Ap

Parsec‐Scale Images of Flat‐Spectrum Radio Sources in Seyfert Galaxies