  Gorenstein rings are important to mathematical areas as diverse as algebraic
geometry, where they encode information about singularities of spaces, and
homotopy theory, through the concept of model categories.
  In consequence, the study of Gorenstein rings has led to the advent of a
whole branch of homological algebra, known as Gorenstein homological algebra.
  This paper solves one of the open problems of Gorenstein homological algebra
by showing that so-called Gorenstein projective resolutions exist over quite
general rings, thereby enabling the definition of a Gorenstein version of
derived functors.
  An application is given to the theory of Tate cohomology.
