Let $R=R_0 \oplus R_1 \oplus R_2 ...$ be a graded not necessarily commutative algebra over field $k$ and $R$ is generated by $R_1$, $R_0=k$. In commutative situation if one wants free resolution of $R/I$ one can start with Koszul (or KoszulTate) complex. Is there any noncommutative analogs of such explicit free resolution of $R/I$?
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