# Locally solvable algebra

From Encyclopedia of Mathematics

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.

#### References

[1] | N. Jacobson, "Lie algebras" , Interscience (1962) ((also: Dover, reprint, 1979)) |

**How to Cite This Entry:**

Locally solvable algebra.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Locally_solvable_algebra&oldid=32043

This article was adapted from an original article by V.N. Latyshev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article