Cohen structure theorem: Difference between revisions
No edit summary |
|||
| Line 7: | Line 7: | ||
===Symbolic statement=== | ===Symbolic statement=== | ||
Let <math>R</math> be a [[complete local ring|complete local]] [[Noetherian ring]] with [[residue field]] <math>K</math>. If <math>R</math> contains a field, then <math>R = K[[x_1, x_2, \ | Let <math>R</math> be a [[complete local ring|complete local]] [[Noetherian ring]] with [[residue field]] <math>K</math>. If <math>R</math> contains a field, then <math>R = K[[x_1, x_2, \ldots, x_n]]/I</math> for some <math>n</math> and some <math>I</math> | ||
Revision as of 14:32, 7 August 2007
Statement
Verbal statement
Any complete local equicharacteristic Noetherian ring is a quotient of a power series ring over its residue field.
Symbolic statement
Let be a complete local Noetherian ring with residue field . If contains a field, then for some and some