defining relation in Milnor K-theory
C64704
concept
The defining relation in Milnor K-theory is the Steinberg relation, which states that for any field \(F\) and any \(a, b \in F^\times\) with \(a + b = 1\), the symbol \(\{a, b\}\) vanishes in \(K_2^M(F)\), and more generally \(\{a, 1 - a\} = 0\) generates the ideal of relations in the tensor algebra defining \(K_*^M(F)\).
All labels observed (1)
| Label | Occurrences |
|---|---|
| defining relation in Milnor K-theory 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: defining relation in Milnor K-theory
Generated description
The defining relation in Milnor K-theory is the Steinberg relation, which states that for any field \(F\) and any \(a, b \in F^\times\) with \(a + b = 1\), the symbol \(\{a, b\}\) vanishes in \(K_2^M(F)\), and more generally \(\{a, 1 - a\} = 0\) generates the ideal of relations in the tensor algebra defining \(K_*^M(F)\).
Instances (1)
| Instance | Via concept surface |
|---|---|
| Steinberg relations | — |