ring-theoretic structure
C49601
concept
A ring-theoretic structure is an algebraic system consisting of a set equipped with two binary operations, typically addition and multiplication, that satisfy the ring axioms such as associativity, distributivity, and the existence of an additive identity and inverses.
All labels observed (2)
| Label | Occurrences |
|---|---|
| commutative ring with identity | 1 |
| ring-theoretic structure canonical | 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-theoretic structure
Generated description
A ring-theoretic structure is an algebraic system consisting of a set equipped with two binary operations, typically addition and multiplication, that satisfy the ring axioms such as associativity, distributivity, and the existence of an additive identity and inverses.
Instances (2)
| Instance | Via concept surface |
|---|---|
| Dedekind domain | — |
| GF(p) | commutative ring with identity |