  We study the properties of Type Ia Supernovae (SNe Ia) as functions of the
radial distance from their host galaxy centers. Using a sample of 62 SNe Ia
with reliable luminosity, reddening, and decline rate determinations, we find
no significant radial gradients of SNe Ia peak absolute magnitudes or decline
rates in elliptical+S0 galaxies, suggesting that the diversity of SN properties
is not related to the metallicity of their progenitors. We do find that the
range in brightness and light curve width of supernovae in spiral galaxies
extends to brighter, broader values. These results are interpreted as support
for an age, but not metallicity, related origin of the diversity in SNe Ia. If
confirmed with a larger and more accurate sample of data, the age-luminosity
relation would offer a new and powerful tool to probe the ages and age
gradients of stellar populations in galaxies at redshift as high as $z\sim1-2$.
The absence of significant radial gradients in the peak $\rm (B-V)_0$ and $\rm
(V-I)_0$ colors of SNe Ia supports the redding correction method of Phillips et
al (1999). We find no radial gradient in residuals from the SN Ia
luminosity-width relation, suggesting that the relation is not affected by
properties of the progenitor populations and supporting the reliability of
cosmological results based upon the use of SNe Ia as distance indicators.
