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Koszul and homogeneous Koszul algebras were defined by Priddy in\cite{Priddy1970}. There exist some relations between these algebras and theskew PBW extensions introduced in \cite{LezamaGallego}. In this paper we giveconditions to guarantee that skew PBW extensions over fields are Koszul orhomogeneous Koszul. We also show that a constant skew PBW extension of a fieldis a PBW deformation of its homogeneous version.

Koszulity for skew PBW extensions over fields