ring theory
E159882
Ring theory is a branch of abstract algebra that studies rings—algebraic structures equipped with two binary operations generalizing addition and multiplication of integers—and their ideals, modules, and homomorphisms.
All labels observed (1)
| Label | Occurrences |
|---|---|
| ring theory canonical | 1 |
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
branch of mathematics
ⓘ
subfield of abstract algebra ⓘ |
| appliesTo |
algebraic geometry
ⓘ
algebraic topology ⓘ functional analysis ⓘ number theory ⓘ |
| associatedWith |
David Hilbert
ⓘ
Emil Artin ⓘ Emmy Noether ⓘ Joseph Wedderburn ⓘ Richard Dedekind ⓘ |
| developedFrom |
algebraic geometry
ⓘ
number theory ⓘ |
| fieldOfStudy |
ideals
ⓘ
modules ⓘ ring homomorphisms ⓘ rings ⓘ |
| hasSubfield |
commutative algebra
ⓘ
homological algebra ⓘ noncommutative ring theory ⓘ |
| historicalDevelopment | 19th century ⓘ |
| partOf | abstract algebra ⓘ |
| studies |
algebraic structures with two binary operations
ⓘ
generalizations of integer addition and multiplication ⓘ |
| usesConcept |
Artinian rings
ⓘ
Artin–Wedderburn theorem ⓘ Chinese remainder theorem ⓘ Euclidean domains ⓘ Jacobson radical ⓘ Noetherian rings ⓘ associativity ⓘ commutativity ⓘ distributivity ⓘ division rings ⓘ fields ⓘ idempotent elements ⓘ identity elements ⓘ integral domains ⓘ local rings ⓘ maximal ideals ⓘ module theory ⓘ nilpotent elements ⓘ nilradical ⓘ prime ideals ⓘ principal ideal domains ⓘ representation theory of algebras ⓘ semisimple rings ⓘ unique factorization domains ⓘ units ⓘ zero divisors ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.