Locally solvable algebra

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An algebra for which any finitely-generated subalgebra is solvable (cf. Solvable group). It is convenient to represent a locally solvable algebra as the union of an increasing chain of solvable subalgebras. The class of locally solvable algebras is closed with respect to transition to subalgebras and taking homomorphic images.


[1] N. Jacobson, "Lie algebras" , Interscience (1962) ((also: Dover, reprint, 1979))
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Locally solvable algebra. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.N. Latyshev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article