Timeline for The Image of a Derivation is Contained in the Jacobson Radical
Current License: CC BY-SA 4.0
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| Sep 2, 2018 at 16:59 | history | edited | abx | CC BY-SA 4.0 |
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| Sep 2, 2018 at 5:50 | comment | added | Keith Kearnes | The argument is not yet complete: you show that $D(J(A))\subseteq J(A)$, but not that $D(A)\subseteq J(A)$. Continue (in the local case): if $x\in A-J(A)$ does not satisfy $D(x)\in J(A)$, differentiate the minimal polynomial of $x$ over $K$ modulo $J(A)$ to get a contradiction. | |
| Sep 2, 2018 at 3:29 | comment | added | Yemon Choi | This doesn't seem so stupid to me coming from the background of Banach algebras: it's an old result of Singer and Wermer that if A is a unital commutative Banach algebra over the complex field and $D:A\to A$ is a continuous complex-linear derivation, then $D(A)\subseteq J(A)$. | |
| Sep 2, 2018 at 3:21 | history | answered | abx | CC BY-SA 4.0 |