local ring sentence in Hindi
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- Any such subring will be a local ring.
- There are 2-dimensional, regular local ring, and this makes it possible to describe modules over it.
- Cf . the example given at local ring.
- A regular local ring is a UFD.
- Thus the function field of " X " is just the local ring of its generic point.
- A Noetherian local ring is parafactorial if and only if its spectrum is parafactorial along its closed point.
- It is a J-2 ring as all Noetherian local rings of dimension at most 1 are J-2 rings.
- It leads to an important class of commutative rings, the local rings that have only one maximal ideal.
- Local behavior in commutative algebraic geometry is captured by commutative algebra and especially the study of local rings.
- Von Neumann regular rings and primitive rings are semiprimitive, however quasi-Frobenius rings and local rings are usually not semiprimitive.
- Alternatively, one can define the function field in this case to be the local ring of the generic point.
- Proved that if a local ring of an algebraic variety is a normal ring, then it is analytically irreducible.
- A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.
- Another property suggested by geometric intuition is that the localization of a regular local ring should again be regular.
- The Auslander Buchsbaum formula implies that a Noetherian local ring is localization of a regular local ring is regular.
- The Auslander Buchsbaum formula implies that a Noetherian local ring is localization of a regular local ring is regular.
- Other local rings have unique generic and special points, but a more complicated spectrum, since they represent general dimensions.
- Bourbaki used " commutative algebra "; sometimes " local algebra " is applied to the theory of local rings.
- In geometric terms, this holds for a local ring of a subscheme of codimension " c " in a regular scheme.
- Brenner and Trivedi have treated local rings coming from the homogeneous co-ordinate rings of smooth projective curves, using techniques from algebraic geometry.
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