algebra over a field
C17817
concept
An algebra over a field is a vector space equipped with a bilinear multiplication operation that combines vectors to produce another vector in a way compatible with scalar multiplication from the field.
All labels observed (10)
| Label | Occurrences |
|---|---|
| finite-dimensional algebra | 3 |
| algebra | 2 |
| algebra over a field canonical | 2 |
| Banach *-algebra | 1 |
| Hopf algebra | 1 |
| cellular algebra | 1 |
| normed algebra | 1 |
| quadratic algebra | 1 |
| quadratic extension of ℚ | 1 |
| quantum algebra | 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: algebra over a field
Generated description
An algebra over a field is a vector space equipped with a bilinear multiplication operation that combines vectors to produce another vector in a way compatible with scalar multiplication from the field.
Instances (12)
| Instance | Via concept surface |
|---|---|
| Weyl algebra | — |
| Gaussian rationals ℚ(i) | quadratic extension of ℚ |
| C*-algebras | Banach *-algebra |
| Banach algebra | normed algebra |
| Racah algebra | algebra |
| Askey–Wilson algebra | quadratic algebra |
| q-Onsager algebra | quantum algebra |
| Griess algebra | finite-dimensional algebra |
| Clifford algebra | — |
| Drinfeld–Jimbo quantum groups | Hopf algebra |
| Bose–Mesner algebra | finite-dimensional algebra |
| Temperley–Lieb algebra | algebra |