Cohen structure theorem

Statement

Verbal statement

Any complete local equicharacteristic Noetherian ring is a quotient of a power series ring over its residue field.

Symbolic statement

Let $R$ be a complete local Noetherian ring with residue field $K$. If $R$ contains a field, then $R=K[[x_1,x_2,\dots ,x_n]]/I$ for some $n$ and some $I$