Recent content by gurilupi

  1. G

    A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

    Thanks for the link but I am uncertain where to even start the normalization process. The proof you linked says: induct on the number of generators of the ##k##-algebra. So in our case on the three generators of the ideal. Then, you pick one generator, say the first and check whether ##I = k[X_1...
  2. G

    A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

    No, I don't see a polynomial relation between the generators. I suppose you mean that we can somehow remove some indeterminants by substitution?
  3. G

    A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

    I do speak German so there won't be an issue with the language. I'll have a look at it. Thanks.
  4. G

    A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

    That's not an issue since in the course we are assuming our field to be algebraically closed, i.e. infinite. Thus for the purpose of the problem statement we do have that ##k## is infinite. The issue that I have here is that I never seen the actual process of Noether normalization in practice...
  5. G

    A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

    No, it's from Atiyah & Macdonald Introduction to commutative algebra.
  6. G

    A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

    Thanks for the answer. The proof of Nother's Normalization Lemma that I have also uses induction. The issue is that the hypothesis assumes a finitely generated algebra ##A##. So what is my finitely generated algebra and what are the generators?
  7. G

    A How Do You Apply Noether Normalization to a Polynomial Ring Ideal?

    Suppose ##I \subseteq k[X_{1}, X_{2}, X_{3}, X_{4}]## be the ideal generated by the maximal minors of the ##2 \times 3## matrix $$\begin{pmatrix} X_1 & X_2 & X_3\\ X_2 & X_3 & X_4 \end{pmatrix}.$$ I have to find a Noether normalization ##k[Y_1, Y_2, Y_3, Y_4] \subseteq k[X_1, X_2, X_3, X_4]##...
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