Quote:

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 (Crying)

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.