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We study (two-sided) ideals I in the enveloping algebra ${U}(\Fraktur {g}_{\infty })$ of an infinite-dimensional Lie algebra $\Fraktur {g}_{\infty }$ obtained as the union (equivalently, direct limit) of an arbitrary chain of embeddings of simple finite-dimensional Lie algebras $$\Fraktur{g}_1 \rightarrow \Fraktur{g}_2 \rightarrow \cdots\rightarrow \Fraktur{g}_n \rightarrow \cdots $$ with $\lim _{...

On Ideals in the Enveloping Algebra of a Locally Simple Lie Algebra