Timeline for Tensor products of two domains
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 10, 2016 at 14:34 | answer | added | Mark Spivakovsky | timeline score: 3 | |
| Oct 10, 2016 at 13:34 | answer | added | Jason Starr | timeline score: 3 | |
| Oct 10, 2016 at 13:04 | comment | added | Jason Starr | Actually, there are counterexamples . . . | |
| Oct 10, 2016 at 12:31 | comment | added | Pierre MATSUMI | Dear Jason, then could you please explain to me how you use the fraction field of an integral domain is a flat extension in order to reduce the setting into fields case? Thanks. | |
| Oct 10, 2016 at 10:17 | comment | added | Jason Starr | @abx. Perhaps the OP wants to assume that $k(S)$ and $k(T)$ are linearly disjoint as field extensions of $k(R)$. At any rate, this question does not seem to be appropriate for MO. Since the fraction field of an integral domain is a flat ring extension, the question reduces to the question whether $k(T)\otimes_{k(R)} k(S)$ is integral, which it is when $k(S)$ and $k(T)$ are linearly disjoint extensions of $k(R)$. | |
| Oct 10, 2016 at 10:12 | comment | added | abx | What is the meaning of $k(R)=k(S)\cap k(T)$? | |
| Oct 10, 2016 at 9:41 | history | asked | Pierre MATSUMI | CC BY-SA 3.0 |