Galois group of a polynomial: Difference between revisions
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==Definition== | ==Definition== | ||
For <math>K</math> a [[field]], the '''Galois group of a polynomial''' <math>f(X) \in K[X]</math> is defined to be the [[Galois group]] (in the sense of field extensions) of a [[splitting field]] for <math>f(X)</math> over <math>K</math>. | For <math>K</math> a [[field]], the '''Galois group of a polynomial''' <math>f(X) \in K[X]</math> is defined to be the [[Galois group]] (in the sense of field extensions) of a [[splitting field]] for <math>f(X)</math> over <math>K</math>. | ||
Revision as of 20:24, 7 November 2023
This article defines a natural context where a group occurs, or is associated, with another algebraic, topological, analytic or discrete structure
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This term is related to: Galois theory
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Definition
For a field, the Galois group of a polynomial is defined to be the Galois group (in the sense of field extensions) of a splitting field for over .
![{\displaystyle f(X)\in K[X]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/06edc406bb6106da0dc24ab15c140380e23ddff4)
