Milnor ring

In the mathematical discipline known as K-theory, the Milnor ring of a field F, named after John Milnor, is defined ^[1] as the graded ring $K_*^M (F)$ with unit, generated by symbols $\ell(a)$ (for $a \in F -\{0\}$ of degree one, with relations

$\ell(ab)=\ell(a)+\ell(b),\quad \ell(a)\ell(1-a)=0. \,$

One can show that $K_0^M (F)={\mathbb Z}$, $K_1^M (F)=F -\{0\}$.

The Milnor ring appears as one side of the Milnor conjecture.

References

1. ^ T.A. Springer, A remark on the Milnor ring, Inventiones mathematicae, 1970

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