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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
-2
votes
A proof for a statement about polynomial automorphism
The very short proof I have is as follows.
Suppose that $\Phi: k[x_1,...,x_n] \rightarrow k[y_1,...,y_n]$ is surjective then we have an isomorphism $k[x_1,...,x_n]/I \cong k[y_1,...,y_n]$ for some i …
2
votes
4
answers
2k
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A proof for a statement about polynomial automorphism
I already got a proof for the fact that if a polynomial map is surjective then it is also injective. However, I used the invariant dimension of a ring and I want a simpler proof. Bravo for any try. Fo …