  The emissivity for the neutrino pair synchrotron radiation in strong magnetic
fields has been calculated both analytically and numerically for high densities
and moderate temperatures, as can be found in neutron stars. Under these
conditions, the electrons are relativistic and degenerate. We give here our
results in terms of an universal function of a single variable. For two
different regimes of the electron gas we present a simplified calculation and
compare our results to those of Kaminker et al. Agreement is found for the
classical region, where many Landau levels contribute to the emissivity , but
some differences arise in the quantum regime. One finds that the emissivity for
neutrino pair synchrotron radiation is competitive, and can be dominant, with
other neutrino processes for magnetic fields of the order $B \sim 10^{14} -
10^{15} G $.This indicates the relevance of this process for some astrophysical
scenarios, such as neutron stars and supernovae.
