Using new observations for a sample of 931 early-type galaxies, we investig
ate whether the Mg-2-sigma(0) relation shows any dependence on the local en
vironment. The galaxies have been assigned to three different environments
depending on the local overdensity (clusters, groups, and field); we used o
ur complete redshift database to guide the assignment of galaxies. It is fo
und that cluster, group, and field early-type galaxies follow almost identi
cal Mg-2-sigma(0) relations, with the largest Mg-2 zero-point difference (c
lusters minus field) being only 0.007 +/- 0.002 mag. No correlation of the
residuals is found with the morphological type or the bulge-to-disk ratio.
Using stellar population models in a differential fashion, this small zero-
point difference implies a luminosity-weighted age difference of only simil
ar to 1 Gyr between the corresponding stellar populations, with field galax
ies being younger. The mass-weighted age difference could be significantly
smaller if minor events of late star formation took place preferentially in
field galaxies. We combine these results with the existing evidence for th
e bulk of stars in cluster early-type galaxies having formed at very high r
edshift and conclude that the bulk of stars in galactic spheroids had to fo
rm at high redshifts (z greater than or similar to 3), no matter whether su
ch spheroids now reside in low- or high-density regions. The cosmological i
mplications of these findings are briefly discussed.