Originally Posted by
Shurelia Can someone help me to finish my essay pleasee..
this is the lemma:
Let R be a semiprime ring. if axb=0 for all x \in R, then bxa=0.
its from:
M.Bresar, Jordan mappings of semiprime rings, J. Algebra 17 (1989), 218-228
i can't find that journal
you don't need the journal. the proof is very easy: let $\displaystyle y \in R$. since $\displaystyle axb=0$ for all $\displaystyle x \in R$, we have
$\displaystyle (bya)x(bya) =by(axb)ya = 0$,
for all $\displaystyle x \in R$. thus $\displaystyle bya = 0$ because R is semiprime.