# Solvable

In mathematics, solvable may refer:

• Solvable group
• Solvable extension, a field extension whose Galois group is a solvable group
• Solvable equation does not refer to an equation which has solutions, but to a polynomial equation which may by solved by radicals, or, equivalently, has a solvable Galois group
• Solvable Lie algebra
• Solvable problem, a computational problem that can be solved by a Turing machine
• Exactly solvable model

### Other articles related to "solvable":

Cartan's Criterion For Solvability
... of a finite dimensional vector space over a field of characteristic zero is solvable if and only if whenever The fact that in the solvable case follows immediately from Lie's ... Lie algebra over a field of characteristic zero is solvable if and only if (where K is the Killing form) ...
Radical Of A Lie Algebra - Definition
... A maximal solvable ideal, which is called the radical, exists for the following reason ... Firstly let and be two solvable ideals of ... Then is again an ideal of, and it is solvable because it is an extension of by ...
Supersolvable Group - Definition
... By contrast, for a solvable group the definition requires each quotient to be abelian ... As every finite solvable group is polycyclic, this can be seen as one of the key differences between the definitions ... For a concrete example, the alternating group on four points, is solvable but not supersolvable ...
Solvable Lie Algebra - Solvable Lie Groups
... The terminology arises from the solvable groups of abstract group theory ... There are several possible definitions of solvable Lie group ... group termination of the closures of the derived series having a solvable Lie algebra ...

### Famous quotes containing the word solvable:

The problems of the world, AIDS, cancer, nuclear war, pollution, are, finally, no more solvable than the problem of a tree which has borne fruit: the apples are overripe and they are falling—what can be done?... Nothing can be done, and nothing needs to be done. Something is being done—the organism is preparing to rest.
David Mamet (b. 1947)