Difference between revisions of "Locally solvable algebra"
From Encyclopedia of Mathematics
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An [[Algebra|algebra]] for which any finitely-generated subalgebra is solvable (cf. [[Solvable group|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. | An [[Algebra|algebra]] for which any finitely-generated subalgebra is solvable (cf. [[Solvable group|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==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> N. Jacobson, "Lie algebras" , Interscience (1962) ((also: Dover, reprint, 1979))</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> N. Jacobson, "Lie algebras" , Interscience (1962) ((also: Dover, reprint, 1979))</TD></TR></table> | ||
Latest revision as of 14:51, 1 May 2014
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
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