  We associate to a localizable module a left retraction of algebras; it is a
homological ring epimorphism that preserves singularity categories. We study
the behavior of left retractions with respect to Gorenstein homological
properties (for example, being Gorenstein algebras or CM-free).
  We apply the results to Nakayama algebras. It turns out that for a connected
Nakayama algebra $A$, there exists a connected self-injective Nakayama algebra
$A'$ such that there is a sequence of left retractions linking $A$ to $A'$; in
particular, the singularity category of $A$ is triangle equivalent to the
stable category of $A'$. We classify connected Nakayama algebras with at most
three simple modules according to Gorenstein homological properties.
