  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.
