Timeline for Complete subring of F_p[[X]]
Current License: CC BY-SA 3.0
4 events
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| Jun 17, 2016 at 15:56 | answer | added | js21 | timeline score: 5 | |
| Jun 17, 2016 at 13:02 | comment | added | Pierre MATSUMI | Laurent Moret-Bailey teaches us the following. That is, choose the unique maximal ideal $J$ of $A$. Then $A$ is $J$-adically complete and separated. Let $M$ be an $A$-module. If $M$ is $J$-adically complete and separated and $M/JM$ is finitely generated, then $M$ is finitely generated. We apply this to $M={\Bbb F}_p[[X]]$, and we have always $M/JM$ is a finite-dimensional ${\Bbb F}_p$-vector space. This means that $\iota_A$ is ''finite'', which (perhaps) means that $A$ has the Krull-dimension one without noetherian assumption of $A$. Is it obvious that $A$ is noetherian? | |
| Jun 17, 2016 at 12:59 | history | edited | Pierre MATSUMI | CC BY-SA 3.0 |
added 2 characters in body
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| Jun 17, 2016 at 12:35 | history | asked | Pierre MATSUMI | CC BY-SA 3.0 |