# zbMATH — the first resource for mathematics

Correspondence between maximal ideals in associative algebras and Lie algebras. (English) Zbl 0678.17005
Proc. Winter Sch. Geom. Phys., Srní/Czech. 1988, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 21, 343-347 (1989).
[For the entire collection see Zbl 0672.00006.]
The paper considers a commutative associative algebra A with a unit element over a field K of characteristic zero and a subalgebra $$L\subset Der(A)$$ which is an A-submodule such that $$LA=A$$. A natural bijection between the set of all maximal invariant ideals in A and the set of all maximal ideals in L is exhibited.
This result leads to the description of all maximal invariant ideals in the real algebra $$C^{\infty}(V)$$, where V is a connected paracompact $$C^{\infty}$$ manifold.
Reviewer: M.Modugno
##### MSC:
 17B05 Structure theory for Lie algebras and superalgebras 16Dxx Modules, bimodules and ideals in associative algebras