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A primitive ideal of $${\mathcal U(G}[X])$$ contracting to a primitive ideal of $${\mathcal U(G)}$$. (Un idéal primitif de $${\mathcal U(G}[X])$$ se contracte en un idéal primitif de $${\mathcal U(G)}$$.) (French) Zbl 0847.17008
Let $${\mathfrak g}$$ be a finite-dimensional Lie algebra over a field of characteristic zero and $$U:= U({\mathfrak g})$$ its enveloping algebra. This paper gives an elementary proof that a primitive ideal of $$U[ x]$$, the polynomial ring in one variable over $$U$$, contracts to a primitive ideal of $$U$$. This may be regarded as a slight strengthening of the well-known fact that $$U$$ is Jacobson.
##### MSC:
 17B35 Universal enveloping (super)algebras
##### Keywords:
contraction; Jacobson ring; enveloping algebra; primitive ideal
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