Question

If L is finite extension of characteristic p field K with $gcd([L:K],p)=1$, show L is separable.

score 1.4k · Answer 1 · 2026-03-25 09:30:02

1.4k

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If L is finite extension of characteristic p field K with $gcd([L:K],p)=1$, show L is separable.

Published on 25 Mar 2026 - 9:30

score 645 · Answer 2 · 2026-03-22 14:21:24

645

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Why does the cube root of a polynomial in a finite field produce a different polynomial when re-cubed?

Published on 22 Mar 2026 - 14:21

score 85 · Answer 3 · 2026-03-19 19:14:55

85

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Frobenius map, zeta functions of a variety over $\mathbb{F}_p$

Published on 19 Mar 2026 - 19:14

score 65 · Answer 4 · 2026-03-25 04:19:10

65

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proof if $P(\alpha$)=0 and $\alpha^i\neq 1$ then $P$ is irreducible

Published on 25 Mar 2026 - 4:19

score 124 · Answer 5 · 2018-03-26 16:28:35

124

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$x^3+2x+2 \in \mathbb{F}_3[x]$. Let $\alpha$ be a root in some extension field.

Published on 26 Mar 2018 - 16:28

score 46 · Answer 6 · 2026-03-25 06:01:59

46

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understanding a theorem related to Hensel lifting

Published on 25 Mar 2026 - 6:01

score 354 · Answer 7 · 2018-03-27 01:57:31

354

Views

Galois $\text{GF}(5)$, does $α^4=2$ make any sense?

Published on 27 Mar 2018 - 1:57

score 30 · Answer 8 · 2018-03-27 18:05:39

30

Views

For the following linear mapping, determine a transformation matrix and check for the property of injectivity.

Published on 27 Mar 2018 - 18:05

score 153 · Answer 9 · 2026-03-25 09:27:18

153

Views

confused about $\Bbb F_3(\alpha) \cong \Bbb F_3/\langle x^3+2x+2\rangle$

Published on 25 Mar 2026 - 9:27

score 84 · Answer 10 · 2026-03-25 03:22:57

84

Views

What is $(x^7-x)mod(x^6-3)$ equal to?

Published on 25 Mar 2026 - 3:22

score 140 · Answer 11 · 2026-03-25 09:49:22

140

Views

Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

Published on 25 Mar 2026 - 9:49

score 167 · Answer 12 · 2026-03-25 11:06:55

167

Views

About number of algebra of dimension 2 over a field

Published on 25 Mar 2026 - 11:06

score 502 · Answer 13 · 2026-03-25 03:36:06

502

Views

Galois extension from $GF(5)$ to $GF(25)$.

Published on 25 Mar 2026 - 3:36

score 83 · Answer 14 · 2026-03-25 03:22:52

83

Views

A question on Finite fields and irreducible polynomials.

Published on 25 Mar 2026 - 3:22

score 234 · Answer 15 · 2026-03-25 07:45:05

234

Views

Given finite field projections of a rational, can I find the original rational?

Published on 25 Mar 2026 - 7:45

List Question

If L is finite extension of characteristic p field K with $gcd([L:K],p)=1$, show L is separable.

Why does the cube root of a polynomial in a finite field produce a different polynomial when re-cubed?

Frobenius map, zeta functions of a variety over $\mathbb{F}_p$

proof if $P(\alpha$)=0 and $\alpha^i\neq 1$ then $P$ is irreducible

$x^3+2x+2 \in \mathbb{F}_3[x]$. Let $\alpha$ be a root in some extension field.

understanding a theorem related to Hensel lifting

Galois $\text{GF}(5)$, does $α^4=2$ make any sense?

For the following linear mapping, determine a transformation matrix and check for the property of injectivity.

confused about $\Bbb F_3(\alpha) \cong \Bbb F_3/\langle x^3+2x+2\rangle$

What is $(x^7-x)mod(x^6-3)$ equal to?

Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

About number of algebra of dimension 2 over a field

Galois extension from $GF(5)$ to $GF(25)$.

A question on Finite fields and irreducible polynomials.

Given finite field projections of a rational, can I find the original rational?

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