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Posted 2022-03-29Updated 2023-01-03Algebra / Group Theory / Galois Theory

Examples in Galois Theory 3 - Polynomials of Prime Degree and Pairs of Nonreal Roots

In this episode we focus on the rational field. What can we know about the Galois group of an irreducible polynomial with prime degree? There is a method by counting the number of nonreal roots. From this, we obtain an algorithm to compute the Galois group.
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Posted 2022-03-27Updated 2022-03-27Algebra / Group Theory / Galois Theory

Examples in Galois Theory 2 - Cubic Extensions

We study the Galois group of a cubic polynomial over a field with characteristic not equal to 2 and 3.
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Posted 2022-03-16Updated 2022-03-24Algebra / Group Theory / Galois Theory

Examples in Galois Theory 1 - Complex Field is Algebraically Closed

We try to prove the fundamental theorem of algebra, that the complex field is algebraically closed, using as little analysis as possible. In other words, the following proof will be *almost* algebraic.
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Desvl

Desvl

A blog mainly on graduate mathematics.

A Noetherian local ring

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