# Enveloping algebra of a Lie algebra

Let $U(L)$ be the enveloping algebra of a Lie algebra $L$. How can I prove that $U(L)$ hasn't zero divisiors (e.g. if $xy=0$, $x,y \in U(L)$ then $x=0$ or $y=0$)?

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Do you have any assumption on $\rm L$ ? –  Damien L Feb 15 '13 at 21:54
Not... it is only a Lie algera. –  ArthurStuart Feb 15 '13 at 21:56

I doubt it. ${}$ –  Mariano Suárez-Alvarez Feb 15 '13 at 22:03