A Short Proof for the Krull Dimension of a Polynomial Ring

@article{Coquand2005ASP,
  title={A Short Proof for the Krull Dimension of a Polynomial Ring},
  author={Thierry Coquand and Henri Lombardi},
  journal={The American Mathematical Monthly},
  year={2005},
  volume={112},
  pages={826-829}
}
  • Thierry Coquand, Henri Lombardi
  • Published in
    The American Mathematical…
    2005
  • Mathematics, Computer Science
  • Since the other inclusion is trivial, we get N = Y-=I Rni + aL. It follows that N is finitely generated, which contradicts the definition of N. Therefore p is a prime ideal. Since M is finitely generated, we have M/N = Rxj + ... + Rx, for some x,..., x, in M, where x signifies the equivalence class of x in M/N, hence p = n=IAnn(R ). Because p is a prime ideal, p = Ann(Rij) for some j. Suppose that the set {yi + rixj }, generates N + Rxj, where yi is in N and ri in R. By an argument similar to… CONTINUE READING

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    References

    Publications referenced by this paper.
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