Arf rings
E654173
Arf rings are a class of commutative rings introduced by Turkish mathematician Cahit Arf in his work on algebraic number theory and singularity theory, notable for their role in resolving certain types of singularities.
Statements (27)
| Predicate | Object |
|---|---|
| instanceOf |
class of commutative rings
ⓘ
mathematical concept ⓘ |
| appliesTo | one-dimensional analytically irreducible local domains ⓘ |
| characterizedBy |
conditions on value semigroup
ⓘ
stability under blowing up of ideals ⓘ |
| context |
one-dimensional local domains
ⓘ
valuation theory ⓘ |
| developedIn | 20th century ⓘ |
| field |
algebraic number theory
ⓘ
commutative algebra ⓘ singularity theory ⓘ |
| goal |
control of multiplicity sequences of singularities
ⓘ
simplification of resolution processes ⓘ |
| hasOrigin |
study of algebraic function fields
ⓘ
study of plane curve singularities ⓘ |
| influenced |
later work on numerical semigroups
ⓘ
later work on singularity resolution techniques ⓘ |
| introducedBy | Cahit Arf NERFINISHED ⓘ |
| namedAfter | Cahit Arf NERFINISHED ⓘ |
| property | commutative ⓘ |
| relatedTo |
Arf closure
ⓘ
Arf invariant NERFINISHED ⓘ integral closure of rings ⓘ numerical semigroups ⓘ |
| usedIn |
algebraic geometry
ⓘ
resolution of singularities ⓘ study of curve singularities ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.