Timeline for Flatness and tensor product of rings
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 21, 2013 at 13:58 | vote | accept | Werner Thumann | ||
| Apr 21, 2013 at 10:41 | comment | added | Sasha | Use free resolution $$ 0 \to {\mathbb Z}[x_1,x_2] \xrightarrow{x_1-x_2} {\mathbb Z}[x_1,x_2] \to {\mathbb Z}[x] \to 0 $$ to compute $Tor_1^{{\mathbb Z}[x_1,x_2]}({\mathbb Z}[x],{\mathbb Z}[x]) = {\mathbb Z}[x] \ne 0$. | |
| Apr 21, 2013 at 9:17 | comment | added | Werner Thumann | Thx for your answer. Do you have a reference or easy argument why Z[x] is not flat over Z[x1,x2]? | |
| Apr 21, 2013 at 8:42 | history | answered | Sasha | CC BY-SA 3.0 |