  Pre-Koszul and Koszul algebras were defined by Priddy. There exist some
relations between these algebras and the skew PBW extensions defined. We have
established conditions to guarantee that skew PBW extensions over fields it
turns out homogeneous pre-Koszul or Koszul algebra. In this paper we complement
these results defining graded skew PBW extensions and showing that if R is a
finite presented Koszul K-algebra then every graded skew PBW extension of R is
Koszul.
