Timeline for Closedness of the range of the distorsion of the multiplicative monoid of a number field
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15, 2017 at 22:24 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
added some context
|
| May 15, 2017 at 17:50 | comment | added | Salvo Tringali | So, I seem to understand that you have in mind some kind of convergence in a (hypothetical) "space of monoids", with the convergence being compatible, in some sense, with the "structure behind my question". If so, I'm skeptical that something like this can be made to work, but I would be more than happy to be proved wrong! | |
| May 15, 2017 at 17:40 | comment | added | Gerhard Paseman | The idea would be to show that limits are preserved in passing from the collection of monoids to the real numbers. If one has a sub collection of monoids M each with real number valuation v (v is easier for me to read than l), then a sub sequence of the v's converging to a limit w may point to a related sequence of monoids M. Hopefully one can build a monoid N out of the M's whose valuation is w. Gerhard "Then This Would Show Closure" Paseman, 2017.05.15. | |
| May 15, 2017 at 17:37 | comment | added | Salvo Tringali | @GerhardPaseman: Many, many things are known, the basic reference for the cancellative, commutative case being Geroldinger and Halter-Koch's monograph. E.g., Proposition 1.4.5.1 in the book carries over to the following: If $(H_i)_{i \in I}$ is a family of Dedekind-finite monoids and $H:=\coprod_{i \in I} H_i$, then ${\sf L}_H(a)=\sum_{i \in I} {\sf L}_{H_i}(a_i)$ for every $a=(a_i)_{i \in I} \in H$. Does this answer your question, at least in part? (It's not so clear to me how you'd like to use this kind of results for the present problem.) | |
| May 15, 2017 at 17:32 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
fixed two more typos
|
| May 15, 2017 at 16:27 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
added an observation about the half-factorial case
|
| May 15, 2017 at 15:40 | comment | added | Gerhard Paseman | Are the effects of obvious constructions known? For example, if you measure the disjoint union (or appropriate amalgam) of two monoids, do you get the max of the measures of each one? You might then get closure by taking the disjoint union of all of them. If not union, then product maybe? Gerhard "Maybe The Category Is Closed?" Paseman, 2017.05.15. | |
| May 15, 2017 at 15:19 | history | edited | Salvo Tringali | CC BY-SA 3.0 |
fixed a typo
|
| May 15, 2017 at 14:57 | history | asked | Salvo Tringali | CC BY-SA 3.0 |