ring
C6484
concept
A ring is an abstract algebraic structure consisting of a set equipped with two binary operations—addition and multiplication—that generalize arithmetic with properties like associativity, distributivity, and the existence of an additive identity and inverses.
All labels observed (2)
| Label | Occurrences |
|---|---|
| ring canonical | 4 |
| ring invariant | 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: ring
Generated description
A ring is an abstract algebraic structure consisting of a set equipped with two binary operations—addition and multiplication—that generalize arithmetic with properties like associativity, distributivity, and the existence of an additive identity and inverses.
Instances (5)
| Instance | Via concept surface |
|---|---|
| Trinity ring | — |
| Krull dimension | ring invariant |
| Gaussian integers | — |
| Iffland-Ring | — |
| Grothendieck ring | — |