Timeline for Noncommutative Localization "from scratch"
Current License: CC BY-SA 3.0
5 events
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| Dec 2, 2012 at 17:55 | comment | added | Simone Virili | @Martin: the commutative setting is really different!!! The common point of view for localizing a module $M$ on a commutative ring $R$ with respect to a multiplicative subset $\Sigma\subseteq R$ is to view the elements of $\Sigma$ as endomorphisms of $M$ and so take the direct limit of $|\Sigma|$-many copies of $M$ with these transition maps. When $R$ is not commutative you cannot do so if $\Sigma$ is not included in the center $Z(\Sigma)$. This is a non-trivial complication (in concrete situations it makes really a lot of difference, I can give you concrete examples)! | |
| May 21, 2012 at 17:47 | history | edited | David White | CC BY-SA 3.0 |
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| May 21, 2012 at 13:13 | comment | added | Martin Brandenburg | I've asked the same question in the commutative setting here mathoverflow.net/questions/86923 | |
| May 21, 2012 at 12:51 | history | edited | Stephan F. Kroneck | CC BY-SA 3.0 |
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| May 21, 2012 at 12:46 | history | asked | Stephan F. Kroneck | CC BY-SA 3.0 |