Corollary 7
Tag 09VF, permanent. Cite it as [Bourbaki, Tag 09VF].
Lie Groups and Lie Algebras, chapter I, § 2. Enveloping algebra of a Lie algebra
If K is an integral domain and g is a free K-module, the algebra U has no divisors of zero.
G is isomorphic to a polynomial algebra over K (Theorem 1) and is therefore an integral domain (Algebra, Chapter IV, § 1, no. 4, Theorem 1). Hence the corollary (Commutative Algebra, Chapter III, § 2, no. 3, Proposition 1).
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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Cites
- *Commutative Algebra*, Chapter III, § 2, no. 3, Proposition 1 not yet on this site: AC III
- Theorem 1