  We construct Abelian model structures on the category of chain complexes over
a ring $R$, from the notion homological dimensions of modules. Given an integer
$n > 0$, we prove that the left modules over a ringoid $\mathfrak{R}$ with
projective dimension at most $n$ form the left half of a complete cotorsion
pair. Using this result we prove that there is a unique Abelian model structure
on the category of chain complexes where the exact complexes are the trivial
objects and the complexes with projective dimension at most $n$ form the class
of trivially cofibrant objects. In the paper "Cotorsion pairs in C($R$-Mod)",
the authors construct an Abelian model structure on chain complexes, where the
trivial objects are the exact complexes and the class of cofibrant objects is
given by the complexes whose terms are all projective. We extend this result by
finding a new Abelian model structure with the same trivial objects and where
the cofibrant objects are given by the class of complexes whose terms are
modules with projective dimension at most $n$. We also prove similar results
concerning the flat dimension.
