Coefficient field

Definition

Let $R$ be a local ring. A coefficient field for $R$ is a subfield of $R$ such that the mapping from it to the residue field of $R$, obtained by restricting the quotient mapping, is an isomorphism.

Equivalently, it is a subfield of $R$ that intersects the maximal ideal trivially and whose sum with the maximal ideal is the whole of $R$.