Übersetzung für '
local ring' von Englisch nach Deutsch
21 Übersetzungen
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Anwendungsbeispiele Englisch
weitere Beispiele ...
- Currently, following Jean-Pierre Serre, a multiplicity is generally defined as the length of a local ring associated with the point where the multiplicity is considered.
- A non-Archimedean local field can be viewed as the field of fractions of the completion of the local ring of a one-dimensional arithmetic scheme of rank 1 at its non-singular point.
- In particular a Noetherian local ring is Zariski with respect to the maximal ideal.
- The ring of formal power series with coefficients in a complete local ring satisfies the Weierstrass preparation theorem.
- A local ring has Krull dimension 0 if and only if every element of its maximal ideal is nilpotent.
- Azumaya algebras generalize the notion of central simple algebras to a commutative local ring.
- The dual numbers form a commutative algebra of dimension two over the reals, and also an Artinian local ring. They are one of the simplest examples of a ring that has nonzero nilpotent elements.
- , that is, a prime ideal, then the stalk of the structure sheaf at "P" equals the localization of "R" at the ideal "P", and this is a local ring.
- Serre proved this for all regular local rings. He established the following three properties when "R" is either of equal characteristic or of mixed characteristic and unramified (which in this case means that characteristic of the residue field is not an element of the square of the maximal ideal of the local ring), and conjectured that they hold in general.
- See local ring, perfect ring and Dedekind ring.
- Since [...] is again a complete local ring, the result can be iterated and therefore gives similar factorization results for formal power series in several variables.
- are local rings (i.e. they have unique maximal ideals).
- For an irreducible and reduced curve and a point [...] we can define [...] algebraically as the length of [...] where [...] is the local ring at "P" and [...] is its integral closure.
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