noncommutative ring
C49572
concept
A noncommutative ring is an algebraic structure consisting of a set equipped with two binary operations, addition and multiplication, where addition forms an abelian group, multiplication is associative and distributes over addition, but multiplication need not be commutative.
All labels observed (2)
| Label | Occurrences |
|---|---|
| infinite-dimensional algebra | 1 |
| noncommutative ring 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: noncommutative ring
Generated description
A noncommutative ring is an algebraic structure consisting of a set equipped with two binary operations, addition and multiplication, where addition forms an abelian group, multiplication is associative and distributes over addition, but multiplication need not be commutative.
Instances (2)
| Instance | Via concept surface |
|---|---|
| Hurwitz quaternions | — |
| q-Onsager algebra | infinite-dimensional algebra |