Question

Is a separable extension of an extension field also a separable extension of the base/ground field?

score 809 · Answer 1 · 2026-04-09 13:38:21

809

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Is a separable extension of an extension field also a separable extension of the base/ground field?

Published on 09 Apr 2026 - 13:38

score 84 · Answer 2 · 2026-04-14 10:01:20

84

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simplifying root fields / splitting field on Pinter 31.A.4 problem

Published on 14 Apr 2026 - 10:01

score 1k · Answer 3 · 2026-04-15 00:17:25

1k

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How to find the multiplicative inverse of $a+b\sqrt{2}$ in $\mathbb{Q}({\sqrt{2}})$

Published on 15 Apr 2026 - 0:17

score 41 · Answer 4 · 2026-04-10 08:59:16

41

Views

How to prove that...?

Published on 10 Apr 2026 - 8:59

score 61 · Answer 5 · 2026-04-16 21:47:13

61

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Let $K$ be a field of characteristic $p$. Show that there is a unique ring homomorphism $\mathbb{F}_p\to K$.

Published on 16 Apr 2026 - 21:47

score 107 · Answer 6 · 2026-04-16 15:26:07

107

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Why is it impossible for the mapping $x\mapsto 1/x$ to be a polynomial in an infinite field?

Published on 16 Apr 2026 - 15:26

score 23 · Answer 7 · 2026-04-17 15:46:33

Let $p(x)$ be irreducible in $K[x]$ & $p(x)|(r_1(x)...r_n(x))$ where $r_i(x) \in K[x] \forall 1 \leq i \leq n$. Then $p(x)|r_i(x)$ ...

score 72 · Answer 8 · 2026-03-25 11:54:04

72

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Fields of prime characteristic in which an irreducible polynomial has a root of multiplicity > 1

Published on 25 Mar 2026 - 11:54

score 42 · Answer 9 · 2026-04-15 02:10:10

42

Views

abstract algebra field subring

Published on 15 Apr 2026 - 2:10

score 96 · Answer 10 · 2026-04-04 15:03:55

96

Views

Minimal polynomial for trig function

Published on 04 Apr 2026 - 15:03

score 60 · Answer 11 · 2026-04-16 07:56:05

Let $p$ be prime. What is the biggest number $m$ such that $\{1,\zeta_p,\zeta_p^2,...,\zeta_p^m\}$ is linearly independent over $\mathbb{Q}$?

score 1.5k · Answer 12 · 2026-03-28 14:44:25

1.5k

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Galois group of $x^5-x-1$ over $\Bbb Q$

Published on 28 Mar 2026 - 14:44

score 163 · Answer 13 · 2026-04-14 15:33:04

163

Views

Finite rings $R$ in which $x^{25}=x$ holds

Published on 14 Apr 2026 - 15:33

score 138 · Answer 14 · 2026-04-15 03:54:36

138

Views

Why do we have this bound on the size of this Galois group? Doesn't the argument imply equality here?

Published on 15 Apr 2026 - 3:54

score 70 · Answer 15 · 2026-03-25 01:31:11

70

Views

What is the number/structure of units in a function field over $\mathbb{F}_q$?

Published on 25 Mar 2026 - 1:31

List Question

Is a separable extension of an extension field also a separable extension of the base/ground field?

simplifying root fields / splitting field on Pinter 31.A.4 problem

How to find the multiplicative inverse of $a+b\sqrt{2}$ in $\mathbb{Q}({\sqrt{2}})$

How to prove that...?

Let $K$ be a field of characteristic $p$. Show that there is a unique ring homomorphism $\mathbb{F}_p\to K$.

Why is it impossible for the mapping $x\mapsto 1/x$ to be a polynomial in an infinite field?

Let $p(x)$ be irreducible in $K[x]$ & $p(x)|(r_1(x)...r_n(x))$ where $r_i(x) \in K[x] \forall 1 \leq i \leq n$. Then $p(x)|r_i(x)$ ...

Fields of prime characteristic in which an irreducible polynomial has a root of multiplicity > 1

abstract algebra field subring

Minimal polynomial for trig function

Let $p$ be prime. What is the biggest number $m$ such that $\{1,\zeta_p,\zeta_p^2,...,\zeta_p^m\}$ is linearly independent over $\mathbb{Q}$?

Galois group of $x^5-x-1$ over $\Bbb Q$

Finite rings $R$ in which $x^{25}=x$ holds

Why do we have this bound on the size of this Galois group? Doesn't the argument imply equality here?

What is the number/structure of units in a function field over $\mathbb{F}_q$?

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