Hot core molecules should be detectable in external active galaxies out to high redshift. We present here a detailed study of the chemistry of star-forming regions under physical conditions that differ significantly from those likely to be appropriate in the Milky Way Galaxy. We examine, in particular, the trends in molecular abundances as a function of time with respect to changes in the relevant physical parameters. These parameters include metallicity, dust:gas mass ratio, the H$_{2}$ formation rate, relative initial elemental abundances, the cosmic ray ionization rate, and the temperature of hot cores. These trends indicate how different tracers provide information on the physical conditions and on evolutionary age. We identify hot core tracers for several observed galaxies that are considered to represent spirals, active galaxies, low-metallicity galaxies, and high-redshift galaxies. Even in low-metallicity examples, many potential molecular tracers should be present at levels high enough to allow unresolved detection of active galaxies at high redshift containing large numbers of hot cores.
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