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:

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

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

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

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