Timeline for what are the possible approximations for ideals
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 18, 2014 at 15:21 | comment | added | Dmitry Kerner | or the annihilator of the quotient of two modules | |
| Dec 18, 2014 at 15:20 | comment | added | Dmitry Kerner | If I understand correctly, to understand the integral closure one also needs all the possible projections to DVR's. That's ok for me. My typical scenarios are: the annihilator-of-cokernel for a matrix (a map of free modules) | |
| Dec 15, 2014 at 20:11 | comment | added | Karl Schwede | Reflexification will generally be bigger. I don't think you can see it via projecting to DVRs (unless you want an infinite collection of DVRs, those corresponding to height one primes of your ring). Can you say more about your particular collection of ideals. | |
| Dec 15, 2014 at 20:03 | comment | added | Dmitry Kerner | In my case this is not just one ideal, but an infinite series. Thus the computer is of no use. Are there some shortcuts to compute/estimate the reflexification? Say, maybe it's enough to consider only projections to some DVR's/PID's? Also, what is ("usually") bigger the reflexification or the integral closure? | |
| Dec 15, 2014 at 1:46 | comment | added | Karl Schwede | Reflexification isn't so bad. It's just applying the functor $Hom_R(\bullet, R)$ to the ideal, twice. This can be quite quick in a computer (or at least, usually it isn't the thing that usually kills you in a computer). | |
| Dec 14, 2014 at 20:18 | comment | added | Dmitry Kerner | sorry for being ignorant. What are the simple ways to compute these objects? e.g. given some complicated enough matrix, considered as a morphism of free modules. I'd like to bound (from above) its annihilator-of-cokernel. Or suppose the ideal is defined as the annihilator of the quotient of two (complicated) modules of high rank. Are there some simple ways to compute reflexifications/S2-fications in these cases? | |
| Dec 14, 2014 at 16:38 | history | answered | Karl Schwede | CC BY-SA 3.0 |