Question

$p$ a prime and $p\equiv3\mod 4$, if $a^4=1_F$ where $F$ a field with characteristic $p$, then $x=a+a^{-1}\in F$

score 55 · Answer 1 · 2026-03-25 18:57:51

55

Views

$p$ a prime and $p\equiv3\mod 4$, if $a^4=1_F$ where $F$ a field with characteristic $p$, then $x=a+a^{-1}\in F$

Published on 25 Mar 2026 - 18:57

score 78 · Answer 2 · 2026-03-25 11:25:58

78

Views

Algebraic closure of a real-closed field

Published on 25 Mar 2026 - 11:25

score 151 · Answer 3 · 2026-03-23 03:08:45

151

Views

What implies that $D[X]$ is an UFD?

Published on 23 Mar 2026 - 3:08

score 66 · Answer 4 · 2026-03-26 03:12:46

66

Views

What does it mean to say that A is an $\Bbb F_3$ endomorphism?

Published on 26 Mar 2026 - 3:12

score 122 · Answer 5 · 2026-03-28 02:23:29

122

Views

How to construct a matrix of T with respect to some basis?

Published on 28 Mar 2026 - 2:23

score 1.1k · Answer 6 · 2026-03-25 18:57:52

1.1k

Views

Show that the algebraic closure of $F$ in $K$ is an algebraic closure of $F$.

Published on 25 Mar 2026 - 18:57

score 87 · Answer 7 · 2026-03-19 23:31:06

87

Views

Prove this field extension is separable

Published on 19 Mar 2026 - 23:31

score 2.5k · Answer 8 · 2026-03-25 18:57:50

2.5k

Views

Let $f(x)$ be an irreducible polynomial over $F$ of degree $n$, and let $K$ be a field extension of $F$ with $[K:F]=m$

Published on 25 Mar 2026 - 18:57

score 2.1k · Answer 9 · 2026-03-25 18:56:31

2.1k

Views

Determine the splitting field of $x^4 - 7$ over

Published on 25 Mar 2026 - 18:56

score 286 · Answer 10 · 2026-03-26 04:52:38

286

Views

Element of certain order in multiplicative group

Published on 26 Mar 2026 - 4:52

score 58 · Answer 11 · 2026-03-26 06:29:49

58

Views

Describe $\operatorname{Gal}_F(f)$

Published on 26 Mar 2026 - 6:29

score 38 · Answer 12 · 2026-03-25 04:42:47

38

Views

Help with fixing proof that transcendental extension of $\mathbb{Q}$ is dense in transcendental extension of $\mathbb{Q}_{p}$

Published on 25 Mar 2026 - 4:42

score 14 · Answer 13 · 2018-05-05 07:11:37

14

Views

What about $D$ if $K \cong D$ and $K$ is a good structure?

Published on 05 May 2018 - 7:11

score 165 · Answer 14 · 2026-03-27 15:10:34

165

Views

Let $K$ be a subfield of $\mathbb{C}$ and let $f$ be an irreducible polynomial in $K$. Prove $f$ has no repeated roots in $\mathbb{C}$

Published on 27 Mar 2026 - 15:10

score 42 · Answer 15 · 2026-03-25 18:55:03

42

Views

Extensions field in Galois Theory. Check Proof.

Published on 25 Mar 2026 - 18:55

List Question

$p$ a prime and $p\equiv3\mod 4$, if $a^4=1_F$ where $F$ a field with characteristic $p$, then $x=a+a^{-1}\in F$

Algebraic closure of a real-closed field

What implies that $D[X]$ is an UFD?

What does it mean to say that A is an $\Bbb F_3$ endomorphism?

How to construct a matrix of T with respect to some basis?

Show that the algebraic closure of $F$ in $K$ is an algebraic closure of $F$.

Prove this field extension is separable

Let $f(x)$ be an irreducible polynomial over $F$ of degree $n$, and let $K$ be a field extension of $F$ with $[K:F]=m$

Determine the splitting field of $x^4 - 7$ over

Element of certain order in multiplicative group

Describe $\operatorname{Gal}_F(f)$

Help with fixing proof that transcendental extension of $\mathbb{Q}$ is dense in transcendental extension of $\mathbb{Q}_{p}$

What about $D$ if $K \cong D$ and $K$ is a good structure?

Let $K$ be a subfield of $\mathbb{C}$ and let $f$ be an irreducible polynomial in $K$. Prove $f$ has no repeated roots in $\mathbb{C}$

Extensions field in Galois Theory. Check Proof.

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