Definition 10.160.4. Let $(R, \mathfrak m)$ be a complete local ring. A subring $\Lambda \subset R$ is called a coefficient ring if the following conditions hold:

1. $\Lambda$ is a complete local ring with maximal ideal $\Lambda \cap \mathfrak m$,

2. the residue field of $\Lambda$ maps isomorphically to the residue field of $R$, and

3. $\Lambda \cap \mathfrak m = p\Lambda$, where $p$ is the characteristic of the residue field of $R$.

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