Loading [MathJax]/extensions/tex2jax.js

The Stacks project

Exercise 111.24.2. In each of the following cases determine whether (GU), (GD) holds, and explain why. (Use any Prop/Thm/Lemma you can find, but check the hypotheses in each case.)

  1. $k$ is a field, $A = k$, $B = k[x]$.

  2. $k$ is a field, $A = k[x]$, $B = k[x, y]$.

  3. $A = {\mathbf Z}$, $B = {\mathbf Z}[1/11]$.

  4. $k$ is an algebraically closed field, $A = k[x, y]$, $B = k[x, y, z]/(x^2-y, z^2-x)$.

  5. $A = {\mathbf Z}$, $B = {\mathbf Z}[i, 1/(2 + i)]$.

  6. $A = {\mathbf Z}$, $B = {\mathbf Z}[i, 1/(14 + 7i)]$.

  7. $k$ is an algebraically closed field, $A = k[x]$, $B = k[x, y, 1/(xy-1)]/(y^2-y)$.


Comments (0)


Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.