Question

Finding a basis for a field

score 1.1k · Answer 1 · 2016-05-29 13:17:18

1.1k

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Finding a basis for a field

Published on 29 May 2016 - 13:17

score 312 · Answer 2 · 2016-05-30 12:41:36

312

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I want to show how many intermediate fields there are between $GF(3^{12})$ and $GF(3^4)$.

Published on 30 May 2016 - 12:41

score 245 · Answer 3 · 2026-03-28 22:37:55

245

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$\mathbb{F_2}(\alpha)/\mathbb{F_2}$ is a splitting field of $f(x)$ over $\mathbb{F_2}$

Published on 28 Mar 2026 - 22:37

score 1.3k · Answer 4 · 2016-05-31 22:38:37

1.3k

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Splitting field of $x^9-x$ over $\mathbb{Z}_3$.

Published on 31 May 2016 - 22:38

score 196 · Answer 5 · 2026-03-28 15:20:13

196

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Is there an algorithm to find the splitting field of a polynomial over galois finite fields?

Published on 28 Mar 2026 - 15:20

score 123 · Answer 6 · 2016-06-01 15:18:23

123

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Show that the simple extension $K(X)$ of $K$ has intermediate fields $K \varsubsetneqq F \varsubsetneqq K(X)$.

Published on 01 Jun 2016 - 15:18

score 106 · Answer 7 · 2016-06-01 21:43:38

106

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Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$

Published on 01 Jun 2016 - 21:43

score 4.9k · Answer 8 · 2016-06-02 01:20:06

4.9k

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Non-separable, infinite field extensions of non-zero characteristic

Published on 02 Jun 2016 - 1:20

score 1k · Answer 9 · 2026-04-12 03:28:08

1k

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Zech Logarithms

Published on 12 Apr 2026 - 3:28

score 382 · Answer 10 · 2016-06-03 04:19:29

382

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Sums involving binomial coefficients in a finite field

Published on 03 Jun 2016 - 4:19

score 711 · Answer 11 · 2026-04-12 05:11:11

711

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How To Prove That The Rijndael Polynomial Is Irreducible?

Published on 12 Apr 2026 - 5:11

score 57 · Answer 12 · 2016-06-03 15:42:40

57

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Choose a basis of $\mathbb{F}_q/\mathbb{Z}_p$ to do inverse quickly.

Published on 03 Jun 2016 - 15:42

score 296 · Answer 13 · 2026-03-29 18:11:58

296

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what does $\alpha$ signify in finite fields modular arithmetic

Published on 29 Mar 2026 - 18:11

score 131 · Answer 14 · 2026-03-25 17:37:41

131

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Characters on rings of residue classes modulo polynomials over finite fields

Published on 25 Mar 2026 - 17:37

score 137 · Answer 15 · 2026-04-01 16:31:56

137

Views

Show $|E_1(\mathbb{F_q})|+|E_2(\mathbb{F_q})|=2(q+1)$

Published on 01 Apr 2026 - 16:31

List Question

Finding a basis for a field

I want to show how many intermediate fields there are between $GF(3^{12})$ and $GF(3^4)$.

$\mathbb{F_2}(\alpha)/\mathbb{F_2}$ is a splitting field of $f(x)$ over $\mathbb{F_2}$

Splitting field of $x^9-x$ over $\mathbb{Z}_3$.

Is there an algorithm to find the splitting field of a polynomial over galois finite fields?

Show that the simple extension $K(X)$ of $K$ has intermediate fields $K \varsubsetneqq F \varsubsetneqq K(X)$.

Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$

Non-separable, infinite field extensions of non-zero characteristic

Zech Logarithms

Sums involving binomial coefficients in a finite field

How To Prove That The Rijndael Polynomial Is Irreducible?

Choose a basis of $\mathbb{F}_q/\mathbb{Z}_p$ to do inverse quickly.

what does $\alpha$ signify in finite fields modular arithmetic

Characters on rings of residue classes modulo polynomials over finite fields

Show $|E_1(\mathbb{F_q})|+|E_2(\mathbb{F_q})|=2(q+1)$

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