Arf closure
E654174
Arf closure is a concept in commutative algebra introduced by mathematician Cahit Arf that refines integral closure to better control singularities in one-dimensional local rings and semigroups.
Statements (25)
| Predicate | Object |
|---|---|
| instanceOf |
closure operation
ⓘ
concept in commutative algebra ⓘ |
| appliesTo |
one-dimensional local rings
ⓘ
semigroups ⓘ |
| characteristicProperty | stability under blowing up in dimension one ⓘ |
| context |
curve singularities
ⓘ
one-dimensional analytically irreducible local domains ⓘ |
| ensures | certain regularity conditions on value semigroups ⓘ |
| field | commutative algebra ⓘ |
| generalizes | Arf rings ⓘ |
| goal | to obtain better-behaved singularities than with integral closure alone ⓘ |
| introducedBy | Cahit Arf NERFINISHED ⓘ |
| namedAfter | Cahit Arf NERFINISHED ⓘ |
| purpose | to better control singularities ⓘ |
| refines | integral closure ⓘ |
| relatedTo |
Arf ring
ⓘ
integral closure of ideals ⓘ value semigroup of a curve singularity ⓘ |
| studiedIn |
singularity theory of algebraic curves
ⓘ
theory of numerical semigroups ⓘ |
| typeOf |
closure operation on rings
ⓘ
closure operation on semigroups ⓘ |
| usedFor | resolution of singularities in dimension one ⓘ |
| usedIn |
study of numerical semigroups
ⓘ
study of one-dimensional local rings ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.