  Observations suggest that the properties of Type Ia supernovae (SNe Ia) may
depend on environmental characteristics, such as morphology, metallicity, and
age of host galaxies. The influence of these environmental properties on the
resulting SNe Ia is studied in this paper. First it is shown that the carbon
mass fraction X(C) in the C+O white dwarf SN Ia progenitors tends to be smaller
for lower metallicity and older the binary system age. It is then suggested
that the variation of X(C) causes the diversity in the brightness of SNe Ia: a
smaller X(C) leads to a dimmer SN Ia. Further studies of the propagation of the
turbulent flame are necessary to confirm this relation. Our model for the SN Ia
progenitors then predicts that when the progenitors belong to an older
population or to a low metallicity environment, the number of bright SNe Ia is
reduced, so that the variation in brightness among the SNe Ia is also smaller.
Thus our model can explain why the mean SN Ia brightness and its dispersion
depend on the morphology of the host galaxies and on the distance of the SN
from the center of the galaxy. It is further predicted that at higher redshift
(z >~ 1) both the the mean brightness of SNe Ia and its variation should be
smaller in spiral galaxies than in elliptical galaxies. These variations are
within the range observed in nearby SNe Ia. In so far as the variation in X(C)
is the most important cause for the diversity among SNe Ia, the light curve
shape method currently used to determine the absolute magnitude of SNe Ia can
be applied also to high redshift SNe Ia.
