Timeline for Is a "separable" algebra over a field finite-dimensional?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Jul 16 at 1:18 | answer | added | Wang Chao | timeline score: 0 | |
| Jun 8, 2023 at 15:18 | history | edited | John Baez | CC BY-SA 4.0 |
fixed spelling of "semsimple"
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| Feb 9, 2022 at 14:27 | answer | added | Benjamin Steinberg | timeline score: 7 | |
| Feb 9, 2022 at 14:18 | comment | added | H. E. | @Echo If you mean we take product for all $n$, then it is not semisimple since a semisimple ring must be artinian and noetherian, and the infinite product of non-zero rings is neither artinian nor noetherian. | |
| Feb 9, 2022 at 14:13 | comment | added | H. E. | @ R. van Dobben de Bruyn A ring is semisimple if it is a semisimple module as a left (or equivalently right) A-module, and a semisimple algebra is just a $k$-algebra which is semisimple as a ring. | |
| Feb 9, 2022 at 14:08 | comment | added | user473423 | If you take the product of all matrix algebras $\mathrm{Mat}_n(k)$. Would that be semisimple in your definition? | |
| Feb 9, 2022 at 13:39 | comment | added | R. van Dobben de Bruyn | What definition of semisimple are you using? I know a few different ones, but it's possible that they're only equivalent when you already assume finite-dimensionality. | |
| Feb 9, 2022 at 12:25 | comment | added | H. E. | $A^e$ is the tensor product algebra $A \otimes_k A^{op}$ of $A$ and the opposite algebra $A^{op}$. | |
| Feb 9, 2022 at 12:21 | history | edited | H. E. | CC BY-SA 4.0 |
added 36 characters in body
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| Feb 9, 2022 at 11:12 | comment | added | user473423 | What is the enveloping algebra? I only know this term in the context of Lie algebras. | |
| S Feb 9, 2022 at 2:35 | review | First questions | |||
| Feb 9, 2022 at 2:37 | |||||
| S Feb 9, 2022 at 2:35 | history | asked | H. E. | CC BY-SA 4.0 |