In mathematics, the Cohen structure theorem, introduced by Cohen (1946), describes the structure of complete Noetherian local rings.
Some consequences of Cohen's structure theorem include three conjectures of Krull:
- Any complete regular equicharacteristic Noetherian local ring is a ring of formal power series over a field. (Equicharacteristic means that the local ring and its residue field have the same characteristic, and is equivalent to the local ring containing a field.)
- Any complete regular Noetherian local ring that is not equicharacteristic but is unramified is uniquely determined by its residue field and its dimension.
- Any complete Noetherian local ring is the image of a complete regular Noetherian local ring.