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 $$R$$.