Talk:Alternativity

Untitled

Hello

is there a word for $x(yx)=(xy)x$?

Robinh 13:00, 23 February 2007 (UTC)

The word is flexible. We don't seem to have anything on Wikipedia, but PlanetMath has an entry on flexible algebras. --Zundark 16:54, 23 February 2007 (UTC)

We do now have flexible algebra. —Toby Bartels (talk) 17:34, 9 October 2016 (UTC)

Added the technical tag. Could we maybe add a concrete example (perhaps an alternative ring?) Furthermore in the same vein as the page for Associative, we should maybe describe it in the general sense of arithmetic before moving on to abstract algebra. --140.211.90.206 (talk) 19:30, 8 November 2021 (UTC)

Alternativity implies power associativity

The article currently claims:

In fact, an alternative magma need not even be power-associative: already the expression $(xx)(xx)$ cannot be proven to be identical to expressions such as $(x(x(xx)))$ purely by alternativity.

However this seems false? It seems that with only left-alternativity this can be shown. Restated left-alternativity is $(aa)b=a(ab)$, let $a=x,b=xx$ then this is $(xx)(xx)=x(x(xx))$. The exact statement which it states cannot be proven. I'm removing this claim. Let me know if I am mistaken or misunderstanding. AquitaneHungerForce (talk) 20:34, 10 January 2025 (UTC)