Timeline for non-associative but commutative algebra
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 13, 2020 at 2:24 | comment | added | Andreas Blass | It's not a ring. I understood "algebra" in the sense of universal algebra. If you want it to be understood in the sense of rings and bilinearity, then you should linearize it: Take the vector space with my example as a basis, and extend the midpoint operation from basis vectors to arbitrary vectors by bilinearity. | |
| Jul 12, 2020 at 18:34 | comment | added | Jeremy Rickard | Similarly, you can linearize the NAND operation on $\{T,F\}$ to get a two-dimensional (non-unital) example. Or adjoin a unit to get a three-dimensional unital example. | |
| Jul 12, 2020 at 17:41 | comment | added | Phil Tosteson | Nice example. @Sunny Note this isn't bilinear so to make it into an algebra you need to linearize it, or modify it in some other way. | |
| Jul 12, 2020 at 15:45 | comment | added | Sunny | How it's ring operations? What is the unit element? | |
| Jul 12, 2020 at 15:29 | comment | added | Mirco A. Mannucci | simplex sigillum veri. Very nice Andreas ! | |
| Jul 12, 2020 at 15:25 | comment | added | Andreas Blass | The same operation works in any vector space over any field of characteristic $\neq2$. | |
| Jul 12, 2020 at 15:23 | history | answered | Andreas Blass | CC BY-SA 4.0 |