Timeline for quotient by ideals and fractional ideals
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2018 at 10:10 | comment | added | Pedro | Dear @Mohan, I liked your argument a lot. I was wondering if you could rephrase it in terms of divisors on the corresponding arithmetic curve with a very clear and explicit geometric interpretation. Is this possible? | |
| Jul 6, 2017 at 17:09 | comment | added | Mohan | Please read CRT carefully. It says precisely what you need and I think you have not understood what it means. For example, if $I=P_1^nP_2^m$, then $A/I=A/P_1^n\oplus A/P_2^m=A_{P_1}/{P_1^n}_{P_1}\oplus A_{P_2}/{P_2^m}_{P_2}$. | |
| Jul 6, 2017 at 16:06 | comment | added | Hair80 | Does not apply to this case: $A$ and $A_{P}$ are different rings and $I$ is the intersection of all the $I_{P}$ for all $P$ in $A$ and not only those which divide $I$. | |
| Jul 6, 2017 at 15:34 | comment | added | Mohan | Use Chinese remainder theorem. | |
| Jul 6, 2017 at 14:49 | comment | added | Hair80 | I am sorry but I do not understand completely: I do not see any obvious isomorphism between $A/I$ and $\bigoplus_{P|I}(A_{P}/I_{P})$. Is it what it is suggested to search for? | |
| Jul 6, 2017 at 12:13 | history | answered | Mohan | CC BY-SA 3.0 |