Turkish Journal of Mathematics
Article Title
DOI
10.55730/1300-0098.3226
Abstract
Let $A$ be an algebra over a field $F$ with $(F)\ne 2$. If $A$ is generated as an algebra by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $\Phi:A\times A\to X$, where $X$ is an arbitrary vector space over $F$, the condition that $\Phi(x^2,x)=0 $ for all $x\in A$ implies that $\Phi(xy,z) +\Phi(zx,y) + \Phi(yz,x)=0$ for all $x,y,z\in A$. This is applicable to the question of whether $A$ is zero Lie product determined and is also used in proving that a Jordan homomorphism from $A$ onto a semiprime algebra $B$ is the sum of a homomorphism and an antihomomorphism.
First Page
1691
Last Page
1698
Recommended Citation
BRESAR, MATEJ
(2022)
"Jordan maps and zero Lie product determined algebras,"
Turkish Journal of Mathematics: Vol. 46:
No.
5, Article 5.
https://doi.org/10.55730/1300-0098.3226
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss5/5
