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 · 2026-04-14 23:08:53

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 14 Apr 2026 - 23:08

score 651 · Answer 2 · 2026-05-02 18:41:25

651

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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 02 May 2026 - 18:41

score 94 · Answer 3 · 2026-05-07 05:17:23

94

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

Published on 07 May 2026 - 5:17

score 68 · Answer 4 · 2026-05-10 19:41:51

68

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

Published on 10 May 2026 - 19:41

score 127 · Answer 5 · 2026-04-16 23:52:19

127

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

Published on 16 Apr 2026 - 23:52

score 48 · Answer 6 · 2026-04-11 18:45:11

48

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understanding a theorem related to Hensel lifting

Published on 11 Apr 2026 - 18:45

score 357 · Answer 7 · 2026-04-14 21:54:57

357

Views

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

Published on 14 Apr 2026 - 21:54

score 33 · Answer 8 · 2026-04-14 09:39:45

33

Views

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

Published on 14 Apr 2026 - 9:39

score 155 · Answer 9 · 2026-04-16 05:51:52

155

Views

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

Published on 16 Apr 2026 - 5:51

score 86 · Answer 10 · 2026-04-15 20:36:14

86

Views

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

Published on 15 Apr 2026 - 20:36

score 143 · Answer 11 · 2026-05-10 14:06:37

143

Views

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

Published on 10 May 2026 - 14:06

score 169 · Answer 12 · 2026-04-14 07:40:12

169

Views

About number of algebra of dimension 2 over a field

Published on 14 Apr 2026 - 7:40

score 505 · Answer 13 · 2026-04-22 12:42:14

505

Views

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

Published on 22 Apr 2026 - 12:42

score 86 · Answer 14 · 2026-05-10 19:35:11

86

Views

A question on Finite fields and irreducible polynomials.

Published on 10 May 2026 - 19:35

score 237 · Answer 15 · 2026-05-10 12:42:40

237

Views

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

Published on 10 May 2026 - 12:42

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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