Situation 10.102.1. Here $R$ is a ring, and we have a complex

\[ 0 \to R^{n_ e} \xrightarrow {\varphi _ e} R^{n_{e-1}} \xrightarrow {\varphi _{e-1}} \ldots \xrightarrow {\varphi _{i + 1}} R^{n_ i} \xrightarrow {\varphi _ i} R^{n_{i-1}} \xrightarrow {\varphi _{i-1}} \ldots \xrightarrow {\varphi _1} R^{n_0} \]

In other words we require $\varphi _ i \circ \varphi _{i + 1} = 0$ for $i = 1, \ldots , e - 1$.

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