# galois theory

Published articles for galois theory.

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## The Fundamental Theorem of Algebra (with Galois Theory)

DevFeed: [The Fundamental Theorem of Algebra (with Galois Theory)](<https://devfeed.tech/articles/the-fundamental-theorem-of-algebra-with-galois-theory-40259.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/02/02/the-fundamental-theorem-of-algebra-galois-theory/>)

Published: 2012-02-02T22:42:11Z

Content type: article

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>)

Tags: [field](<https://devfeed.tech/tags/field.md>), [fundamental-theorem-of-algebra](<https://devfeed.tech/tags/fundamental-theorem-of-algebra.md>), [galois-theory](<https://devfeed.tech/tags/galois-theory.md>), [group-theory](<https://devfeed.tech/tags/group-theory.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [polynomials](<https://devfeed.tech/tags/polynomials.md>), [roots](<https://devfeed.tech/tags/roots.md>)

### AI overview

This mathematics post presents a Galois-theoretic proof strategy for the fundamental theorem of algebra. It assumes familiarity with field extensions, Galois theory, and group theory, and develops the argument using splitting fields, an intermediate extension of degree 2, Sylow subgroups, and the Galois correspondence.

### Source excerpt

This post assumes familiarity with some basic concepts in abstract algebra, specifically the terminology of field extensions, and the classical results in Galois theory and group theory. The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem, and in re-proving an established theorem we introduce new concepts and strategies.