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Math Help - Lemma of Semiprime Ring

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by Shurelia View Post
    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 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.
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