commutative algebra concept
C21322
concept
A commutative algebra concept is an abstract mathematical notion involving commutative rings, their ideals, modules, and related structures, used to study algebraic properties that often underlie geometry and number theory.
All labels observed (18)
| Label | Occurrences |
|---|---|
| commutative algebra | 4 |
| commutative ring | 2 |
| concept in commutative algebra | 2 |
| algebraic concept | 1 |
| class of commutative rings | 1 |
| commutative algebra concept canonical | 1 |
| commutative differential graded algebra | 1 |
| concept in ring theory | 1 |
| construction in commutative algebra | 1 |
| ideal in ring theory | 1 |
| ideal of a ring | 1 |
| invariant in commutative algebra | 1 |
| notion in algebraic geometry | 1 |
| notion in commutative algebra | 1 |
| notion in module theory | 1 |
| result in module theory | 1 |
| ring theory concept | 1 |
| ring-theoretic concept | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: commutative algebra concept
Generated description
A commutative algebra concept is an abstract mathematical notion involving commutative rings, their ideals, modules, and related structures, used to study algebraic properties that often underlie geometry and number theory.
Instances (21)
| Instance | Via concept surface |
|---|---|
| Krull dimension | — |
| Hasse invariant | notion in algebraic geometry |
| Castelnuovo–Mumford regularity | invariant in commutative algebra |
| Fitting lemma | result in module theory |
| Fitting ideal | notion in commutative algebra |
| Henselian ring | ring theory concept |
| Henselization | construction in commutative algebra |
|
Sullivan minimal model in rational homotopy theory
surface form:
Sullivan minimal model
|
commutative differential graded algebra |
| Artinian ring | ring-theoretic concept |
| Jacobson radical | ideal of a ring |
|
Euclidean domains
surface form:
Euclidean domain
|
commutative ring |
| Dedekind ideal | ideal in ring theory |
|
Arf
surface form:
Arf rings
|
concept in commutative algebra |
| Arf rings | class of commutative rings |
| Arf closure | concept in commutative algebra |
| Griess algebra | commutative algebra |
| Cohen–Macaulay ring | commutative ring |
| Frobenius endomorphism | algebraic concept |
| Bose–Mesner algebra | commutative algebra |
| Gelfand–Tsetlin algebra | commutative algebra |
| Bernstein center in representation theory | commutative algebra |