\begin{equation} \label{more-morphisms-equation-resolution-new} C'[x_1, \ldots , x_ n]^{\oplus K} \to C'[x_1, \ldots , x_ n]^{\oplus m} \to C'[x_1, \ldots , x_ n] \to B \otimes _ C C' \to 0 \end{equation}
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