  The nature of star formation and Type Ia supernovae (SNIa) in galaxies in the
field and in rich galaxy clusters are contrasted by juxtaposing the build-up of
heavy metals in the universe inferred from observed star formation and
supernovae rate histories with data on the evolution of Fe abundances in the
intracluster medium (ICM). Models for the chemical evolution of Fe in these
environments are constructed, subject to observational constraints, for this
purpose. While models with a mean delay for SNIa of 3 Gyr and standard initial
mass function (IMF) are consistent with observations in the field, cluster Fe
enrichment immediately tracks a rapid, top-heavy phase of star formation --
although transport of Fe into the ICM may be more prolonged and star formation
likely continues to redshifts <1. The source of this prompt enrichment is Type
II supernovae (SNII) yielding at least 0.1 solar masses per explosion (if the
SNIa rate normalization is scaled down from its value in the field according to
the relative number of candidate progenitor stars in the 3-8 solar mass range)
and/or SNIa explosions with short delay times associated with the rapid star
formation mode. Star formation is >3 times more efficient in rich clusters than
in the field, mitigating the overcooling problem in numerical cluster
simulations. Both the fraction of baryons cycled through stars, and the
fraction of the total present-day stellar mass in the form of stellar remnants,
are substantially greater in clusters than in the field.
