List questions from field-theory

Published on 11 Apr 2026 - 20:57

171

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An exercise about field extensions and roots

Published on 09 Apr 2026 - 19:28

45

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How do I prove that there exists an automorphism of order 3?

Published on 13 Apr 2026 - 11:16

892

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Finding a minimal polynomial over $\mathbb{Q}(\sqrt5)$

Published on 15 Apr 2026 - 6:31

546

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Solving quadratic equation in GF(2)

Published on 11 Apr 2026 - 22:53

3.7k

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Field extension of degree two is normal

Published on 11 Apr 2026 - 15:34

269

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Locally compact valued fields of positive characteristic.

Published on 10 Apr 2026 - 22:10

139

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For any two elements $a, b$ in a field of characteristic $p$, $(a+b)^{p^k} = a^{p^k} +b^{p^k}$

Published on 15 Apr 2026 - 19:06

418

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Describe the multiplication in the ring $F[x]/(x^2)$.

Published on 16 Apr 2026 - 6:01

579

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$K(X)$ is not algebraically closed

Published on 17 Apr 2026 - 14:19

369

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Describe the multiplication in the ring $\Bbb Q[x]/(x^2+x+1)$.

Published on 17 Apr 2026 - 7:40

986

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$F =\Bbb Q[x]/(x^2+x+1)$ $E = \{a + bw + cw^2: a,b,c \in \Bbb Q \} \subseteq \Bbb C$ Prove $E \cong F$

Published on 17 Apr 2026 - 12:21

5.9k

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Why $F_2[X]/(X^2+X+1)$ has $4$ elements and what are those?

Published on 16 Apr 2026 - 13:33

335

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Why is $KF$ Galois over F

Published on 14 Apr 2026 - 21:26

167

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Representation of elements in quotient rings

Published on 13 Apr 2026 - 8:30

List Question

Statements - Galois extension

An exercise about field extensions and roots

How do I prove that there exists an automorphism of order 3?

Finding a minimal polynomial over $\mathbb{Q}(\sqrt5)$

Solving quadratic equation in GF(2)

Field extension of degree two is normal

Locally compact valued fields of positive characteristic.

For any two elements $a, b$ in a field of characteristic $p$, $(a+b)^{p^k} = a^{p^k} +b^{p^k}$

Describe the multiplication in the ring $F[x]/(x^2)$.

$K(X)$ is not algebraically closed

Describe the multiplication in the ring $\Bbb Q[x]/(x^2+x+1)$.

$F =\Bbb Q[x]/(x^2+x+1)$ $E = \{a + bw + cw^2: a,b,c \in \Bbb Q \} \subseteq \Bbb C$ Prove $E \cong F$

Why $F_2[X]/(X^2+X+1)$ has $4$ elements and what are those?

Why is $KF$ Galois over F

Representation of elements in quotient rings

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