D = χ ↔ G = G m = K x {\displaystyle {}D=\chi \leftrightarrow G=G_{m}=K^{x}}
K [ X n , … , X m ] {\displaystyle {}K[X_{n},\ldots ,X_{m}]} d ( X i = 1 {\displaystyle {}d(X_{i}=1}
t {\displaystyle {}t} operiert durch Skalarmultipliktion
d ( X i ) = d ↔ ( t d 1 ⋱ 0 0 ⋱ t d n ) {\displaystyle {}d(X_{i})=d\leftrightarrow {\begin{pmatrix}t^{d_{1}}&&&\\&\ddots &&0\\0&&\ddots &\\&&&t^{d_{n}}\end{pmatrix}}}
K [ X , Y ] {\displaystyle {}K[X,Y]} , d ( X ) = 1 , d ( x ) = 2 {\displaystyle {}d(X)=1,\,d(x)=2}
![{\displaystyle {}K[X_{n},\ldots ,X_{m}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/86b8d5436c3aa39eb294e6a3886255aec7db1779)
operiert durch Skalarmultipliktion
![{\displaystyle {}K[X,Y]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2979004ad27b9ba60c428e400cbf04d9f0957730)
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