  The single-degenerate channel for the progenitors of type Ia supernovae (SNe
Ia) are currently accepted, in which a carbon-oxygen white dwarf (CO WD)
accretes hydrogen-rich material from its companion, increases its mass to the
Chandrasekhar mass limit, and then explodes as a SN Ia. Incorporating the
prescription of \citet{HAC99a} for the accretion efficiency into Eggleton's
stellar evolution code and assuming that the prescription is valid for
\emph{all} metallicities, we performed binary stellar evolution calculations
for more than 25,000 close WD binaries with metallicities $Z=0.06, 0.05, 0.04,
0.03, 0.02, 0.01, 0.004, 0.001, 0.0003$ and 0.0001. For our calculations, the
companions are assumed to be unevolved or slightly evolved stars (WD + MS). As
a result, the initial parameter spaces for SNe Ia at various $Z$ are presented
in orbital period-secondary mass ($\log P_{\rm i}, M_{\rm 2}^{\rm i}$) planes.
Our study shows that both the initial mass of the secondary and the initial
orbital period increase with metallicity. Thus, the minimum mass of the CO WD
for SNe Ia decreases with metallicity $Z$. The difference of the minimum mass
may be as large as 0.24 $M_{\odot}$ for different Z.
  Adopting the results above, we studied the birth rate of SNe Ia for various
$Z$ via a binary population synthesis approach. If a single starburst is
assumed, SNe Ia occur systemically earlier and the peak value of the birth rate
is larger for a high $Z$. The Galactic birth rate from the WD + MS channel is
lower than (but comparable to) that inferred from observations. Our study
indicates that supernovae like SN2002ic would not occur in extremely
low-metallicity environments, if the delayed dynamical-instability model in
\citet{HAN06} is appropriate.
