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Abelian Kummer Extension

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#abstract-algebra #algebraic-number-theory #galois-theory
971
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What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?

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#field-theory #galois-theory #extension-field
389
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Decomposition group of a prime ideal and root of polynomials

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#algebraic-number-theory #galois-theory
690
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How often are Galois groups equal to $S_n$?

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#group-theory #galois-theory
886
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Field extension of degree 3 and polynomial roots

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#galois-theory #finite-fields #extension-field #irreducible-polynomials
270
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Sum of roots of unity an algebraic integer proof

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#number-theory #algebraic-number-theory #galois-theory #roots-of-unity #cyclotomic-polynomials
87
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What is the difference between the algebraic function fields and the fields itself

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#abstract-algebra #field-theory #galois-theory
70
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If $\deg(f) > p^k$ then $f$ as an irreducible divisor of degree $> k$

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#abstract-algebra #polynomials #galois-theory #irreducible-polynomials
88
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Finite characteristic splitting fields of low degree polynomials

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#abstract-algebra #reference-request #galois-theory
148
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If $f(x)\in\mathbb{Q}[x]$ of degree $p$ and $\operatorname{Gal}(K/\mathbb{Q})$ has element of order $p$ then $f(x)$ is irreducible.

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#field-theory #galois-theory
59
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Algebraic Extensions

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#field-theory #galois-theory #extension-field
816
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History of the three "impossible" compass-and-straightedge problems

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#field-theory #galois-theory #math-history #geometric-construction
73
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an exercise in Galois theory about polynomials

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#abstract-algebra #galois-theory
2.7k
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On a Proof that the Splitting Field of a Separable Polynomial is Galois

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#abstract-algebra #field-theory #galois-theory #splitting-field
88
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a question about field extensions and tower formula

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#field-theory #galois-theory

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