local ring in a sentence

Examples

1. Alternatively, one can define the function field in this case to be the local ring of the generic point.
2. proved that if a local ring of an algebraic variety is a normal ring, then it is analytically irreducible.
3. A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.
4. Another property suggested by geometric intuition is that the localization of a regular local ring should again be regular.
5. The Auslander Buchsbaum formula implies that a Noetherian local ring is localization of a regular local ring is regular.
6. The Auslander Buchsbaum formula implies that a Noetherian local ring is localization of a regular local ring is regular.
7. Other local rings have unique generic and special points, but a more complicated spectrum, since they represent general dimensions.
8. Bourbaki used " commutative algebra "; sometimes " local algebra " is applied to the theory of local rings.
9. In geometric terms, this holds for a local ring of a subscheme of codimension " c " in a regular scheme.
10. Brenner and Trivedi have treated local rings coming from the homogeneous co-ordinate rings of smooth projective curves, using techniques from algebraic geometry.