Let
R
R
be any ring. We prove that all direct products of flat right
R
R
-modules have finite flat dimension if and only if each finitely generated left ideal of
R
R
has finite projective dimension relative to the class of all
F
\mathcal F
-Mittag-Leffler left
R
R
-modules, where
F
\mathcal F
is the class of all flat right
R
R
-modules. In order to prove this theorem, we obtain a general result concerning global relative dimension. Namely, if
X
\mathcal X
is any class of left
R
R
-modules closed under filtrations that contains all projective modules, then
R
R
has finite left global projective dimension relative to
X
\mathcal X
if and only if each left ideal of
R
R
has finite projective dimension relative to
X
\mathcal X
. This result contains, as particular cases, the well-known results concerning the classical left global, weak and Gorenstein global dimensions.