List questions from field-theory

Published on 02 May 2026 - 2:45

114

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Is it always true that $\deg[F(\alpha): F(\alpha^2)] = 2$, given $\alpha$ has degree 2 over $F$?

Published on 17 Apr 2026 - 11:37

88

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Is it true that any quadratic extension over $F$ has form $F(\sqrt D)$?

Published on 15 Apr 2026 - 8:35

141

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Does imply f and g are relatively prime in K[x], that f- yg is irreducible in K(y)[x]?

Published on 10 May 2026 - 16:13

24

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Check for this Compute Galois groups of the following polynomials

Published on 14 Apr 2026 - 19:23

67

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What is an example of quadratic number field in which $17$ is a prime element?

Published on 12 Apr 2026 - 4:40

157

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Fixed field theorem

Published on 12 Apr 2026 - 7:12

185

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Does Taylor's theorem (Peano's form) generalize to other fields?

Published on 15 Apr 2026 - 5:46

45

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Subfields generated by the rationals and a primitive root of unity.

Published on 25 Mar 2026 - 17:52

118

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Galois Theory: What, Exactly, is a General Polynomial?

Published on 11 Apr 2026 - 8:50

123

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Example of a field on which every irreducible polynomial has degree a power of $p$

Published on 09 Apr 2026 - 15:24

25

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$\frac{g(x)}{f^*(x)}=\sum_{n\geq 0}s_nx^n$ generates recursion

Published on 16 Apr 2026 - 4:49

24

Views

Tensor product of complex function field over complex or real field

Published on 13 Apr 2026 - 21:22

158

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Using cyclotomic polynomials to show a polynomial is irreducible over $\mathbb{Q}$

Published on 16 Apr 2026 - 10:58

162

Views

How does $x^5-5$ factor over $\mathbb{F}_p$ for different values of $p$ mod 5?

Published on 16 Apr 2026 - 15:04

List Question

Why is $D$ of characteristic $p \gt 0$ in this proof?

Is it always true that $\deg[F(\alpha): F(\alpha^2)] = 2$, given $\alpha$ has degree 2 over $F$?

Is it true that any quadratic extension over $F$ has form $F(\sqrt D)$?

Does imply f and g are relatively prime in K[x], that f- yg is irreducible in K(y)[x]?

Check for this Compute Galois groups of the following polynomials

What is an example of quadratic number field in which $17$ is a prime element?

Fixed field theorem

Does Taylor's theorem (Peano's form) generalize to other fields?

Subfields generated by the rationals and a primitive root of unity.

Galois Theory: What, Exactly, is a General Polynomial?

Example of a field on which every irreducible polynomial has degree a power of $p$

$\frac{g(x)}{f^*(x)}=\sum_{n\geq 0}s_nx^n$ generates recursion

Tensor product of complex function field over complex or real field

Using cyclotomic polynomials to show a polynomial is irreducible over $\mathbb{Q}$

How does $x^5-5$ factor over $\mathbb{F}_p$ for different values of $p$ mod 5?

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