# Lemma of Semiprime Ring

• May 7th 2011, 10:22 AM
Shurelia
Lemma of Semiprime Ring
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)
• May 7th 2011, 04:29 PM
NonCommAlg
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 $y \in R$. since $axb=0$ for all $x \in R$, we have

$(bya)x(bya) =by(axb)ya = 0$,

for all $x \in R$. thus $bya = 0$ because R is semiprime.