  During the last three decades, many papers have reported the existence of a
luminosity-metallicity or mass-metallicity (M-Z) relation for all kinds of
galaxies: The more massive galaxies are also the ones with more metal-rich
interstellar medium. We have obtained the mass-metallicity relation at
different lookback times for the same set of galaxies from the Sloan Digital
Sky Survey (SDSS), using the stellar metallicities estimated with our spectral
synthesis code STARLIGHT. Using stellar metallicities has several advantages:
We are free of the biases that affect the calibration of nebular metallicities;
we can include in our study objects for which the nebular metallicity cannot be
measured, such as AGN hosts and passive galaxies; we can probe metallicities at
different epochs of a galaxy evolution.
  We have found that the M-Z relation steepens and spans a wider range in both
mass and metallicity at higher redshifts for SDSS galaxies. We also have
modeled the time evolution of stellar metallicity with a closed-box chemical
evolution model, for galaxies of different types and masses. Our results
suggest that the M-Z relation for galaxies with present-day stellar masses down
to 10^10 solar masses is mainly driven by the star formation history and not by
inflows or outflows.
