List questions from field-theory

Published on 09 Apr 2026 - 12:46

74

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Suppose $\mathbb{F}$ is a field of characteristic $p$. Show that if $a, b \in$ $\mathbb{F}$ and $a^{p}=b^{p}$, then $a=b$

Published on 26 Apr 2026 - 0:15

87

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Rings Trapped Between Fields

Published on 12 Apr 2026 - 13:31

1.3k

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Proof of : If $K$ is a finite extension of $F$, then $o(G(K,F)) \leq [K:F]$

Published on 28 Mar 2026 - 23:33

87

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Every Galois field $F$ of characteristic $p$ is perfect

Published on 14 Apr 2026 - 7:40

71

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Algebraic extension of fields

Published on 13 Apr 2026 - 9:30

279

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Splitting field of $x^3-2$ over $\Bbb Q$ are distinct but isomorphic

Published on 13 Apr 2026 - 21:15

37

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$\mathbb{Z}[X]/(X,3) \cong \mathbb{F}_3$

Published on 14 Apr 2026 - 10:17

166

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Value of $\pi$ modulo a prime

Published on 16 Apr 2026 - 17:37

38

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Why is $k[x^2-1]\cap (x-1) = (x^2-1)$?

Published on 17 Apr 2026 - 2:14

43

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The same result for $\mathbb{C}$ is true for algebraically closed field?

Published on 14 Apr 2026 - 6:29

1k

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Proving that every constructible number is algebraic

Published on 14 Apr 2026 - 9:35

117

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Proof that in a field $x=0$ is equivalent to $x=-x$

Published on 15 Apr 2026 - 4:30

459

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The order of a finite field

Published on 14 Apr 2026 - 22:57

31

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Roots of Unity, Curtis's rep theory text

Published on 15 Apr 2026 - 3:47

List Question

How to get $(ab)1 = (a1)(b1)$ in Galois field?

Suppose $\mathbb{F}$ is a field of characteristic $p$. Show that if $a, b \in$ $\mathbb{F}$ and $a^{p}=b^{p}$, then $a=b$

Rings Trapped Between Fields

Proof of : If $K$ is a finite extension of $F$, then $o(G(K,F)) \leq [K:F]$

Every Galois field $F$ of characteristic $p$ is perfect

Algebraic extension of fields

Splitting field of $x^3-2$ over $\Bbb Q$ are distinct but isomorphic

$\mathbb{Z}[X]/(X,3) \cong \mathbb{F}_3$

Value of $\pi$ modulo a prime

Why is $k[x^2-1]\cap (x-1) = (x^2-1)$?

The same result for $\mathbb{C}$ is true for algebraically closed field?

Proving that every constructible number is algebraic

Proof that in a field $x=0$ is equivalent to $x=-x$

The order of a finite field

Roots of Unity, Curtis's rep theory text

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