Galois theory
Noun
Meaning
group theory applied to the solution of algebraic equations
Source: WordNetHypernyms
Examples
A treatment of Galois theory along these lines by Kaplansky was influential in the recognition of the general structure here.
Shows how generalisations of Galois theory lead to Galois groupoids.
Galois theory allows to prove that, if the angle is not a multiple of 3°, non-real cube roots are unavoidable.
His contributions include the invention of a topological form of the Abel–Ruffini theorem and the initial development of some of the consequent ideas, a work which resulted in the creation of the field of topological Galois theory in the 1960s.
See also Differential Galois theory for a more detailed discussion.
See that article for a number of examples: the case of Galois theory of course is a leading one.