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Let $B$ be a generalized Koszul algebra over a finite dimensional algebra$S$. We construct a bimodule Koszul resolution of $B$ when the projectivedimension of $S_B$ equals 2. Using this we prove a Poincar\'e-Birkhoff-Witt(PBW) type theorem for a deformation of a generalized Koszul algebra. When theprojective dimension of $S_B$ is greater than 2, we construct bimodule Koszulresolutions for generalized smash product algebras obtained from braidingsbetween finite dimensional algebras and Koszul algebras, and then prove the PBWtype theorem. The results obtained can be applied to standard KoszulArtin-Schelter Gorenstein algebras in the sense of Minamoto and Mori.

PBW deformations of Koszul algebras over a nonsemisimple ring