Extensions of Galois Theory
- Inverse problem of Galois theory
- Given a group G, find an extension of the rational number or other field with G as Galois group.
- Differential Galois theory
- The subject in which symmetry groups of differential equations are studied along the lines traditional in Galois theory. This is actually an old idea, and one of the motivations when Sophus Lie founded the theory of Lie groups. It has not, probably, reached definitive form.
- Grothendieck's Galois theory
- A very abstract approach from algebraic geometry, introduced to study the analogue of the fundamental group.
Read more about this topic: Glossary Of Field Theory
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