Timeline for Factorization in Anticommutative Rings
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2022 at 0:27 | comment | added | Insulin69 | Well it looks like I found another research topic! I don't think I have the right kind of mind myself though to figure this out. | |
| Jul 12, 2022 at 22:09 | comment | added | Will Sawin | @Vincent I guess the $\mathbb R^3$ example isn't associative, so maybe actually associativity isn't a problem for this, and Lie algebras form a natural set of examples. | |
| Jul 12, 2022 at 22:05 | comment | added | Vincent | @WillSawin ah good points. But then what are examples? Exterior algebras where the even degrees are artificially set to zero? | |
| Jul 12, 2022 at 18:12 | comment | added | Salvo Tringali | @Insulin69 To my knowledge, very little has been done so far towards the study of factorization in (non-associative) magmas and, more in particular, in non-associative rings (though much depends on what you mean by the "study of factorization"). There is, however, a lot that could be done. | |
| Jul 12, 2022 at 18:12 | comment | added | Will Sawin | @Vincent Lie algebras aren't associative, so it's not clear what factorization would mean in that context (but maybe that's a good notion) and $\bigwedge V$ is not anticommutative in this strong sense because even wedges commute. | |
| Jul 12, 2022 at 14:35 | history | edited | Vincent | CC BY-SA 4.0 |
linked the link to the link from the comments
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| Jul 12, 2022 at 14:33 | comment | added | Vincent | Okay. So they are naturally riddled with zero divisors as $x^2 = 0$ for all $x$ in such a ring. The most prominent examples are probably Lie algebras and exterior algebras $\bigwedge V$ for some vector space $V$. I would expect people have looked at factorization in those examples at least, but I don't know a reference | |
| Jul 12, 2022 at 14:32 | comment | added | Insulin69 | researchgate.net/publication/… | |
| Jul 12, 2022 at 14:31 | comment | added | Insulin69 | @Vincent I mean anticommutative. An example of anticommutative ring is R^3 under the cross product. | |
| Jul 12, 2022 at 14:26 | comment | added | Vincent | Do you have a link to the article of Valdes & Anderson? Also do you really mean anti-commutative ($ab = -ab$) or 'just' non-commutative? | |
| Jul 12, 2022 at 13:40 | history | asked | Insulin69 | CC BY-SA 4.0 |