Let A,B be left (resp. right) ideals in a semiprime ring R. Show that AB = 0 iff BA = 0.
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Expert's answer
2013-02-04T08:48:52-0500
It suffices to prove the “only if”part, so assume AB = 0, where A,B are (say) left ideals. We have (BA)^2 = BABA = 0, so BA = 0 since R issemiprime.
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