Question

Find $G (K/F) $ where $K $ is a splitting field of $t^p-t-a \in F [t] $.

score 117 · Answer 1 · 2026-03-25 11:27:15

117

Views

Find $G (K/F) $ where $K $ is a splitting field of $t^p-t-a \in F [t] $.

Published on 25 Mar 2026 - 11:27

score 35 · Answer 2 · 2026-03-27 23:48:09

35

Views

In a Galois group of $F(a_1,...,a_n)/F $ with $a_i$'s algebraic, where does the $a_i $'s get mapped to

Published on 27 Mar 2026 - 23:48

score 34 · Answer 3 · 2018-05-19 18:37:42

34

Views

Let $\alpha=\sqrt[5]{2}+\sqrt{5}$, show that $\sqrt{5}\in\mathbb{Q}(\alpha)$.

Published on 19 May 2018 - 18:37

score 533 · Answer 4 · 2026-03-28 04:16:59

533

Views

Epimorphism, in the category of commutative rings with unity , with domain a field is an isomorphism?

Published on 28 Mar 2026 - 4:16

score 25 · Answer 5 · 2026-03-27 23:48:08

25

Views

Let $F/K,F'/K'$ be two galois extensions(maybe infinite), $F\subset F',K\subset K'$, is $G(F'/K')\to G(F/K)$ via restriction open map?

Published on 27 Mar 2026 - 23:48

score 507 · Answer 6 · 2026-02-23 01:23:48

507

Views

If $K $ is infinite and $u,v $ are separable and algebraic over $K $ then there is some $a \in K $ such that $K (u+av)=K (u,v) $ proof verification

Published on 23 Feb 2026 - 1:23

score 401 · Answer 7 · 2026-03-25 23:08:29

401

Views

Minimal polynomial of $\alpha+i$ over $\mathbb{Q}$

Published on 25 Mar 2026 - 23:08

score 192 · Answer 8 · 2026-03-26 06:21:35

192

Views

How many subfields of order $p^m$ in $\mathbb{F}_{p^n}$

Published on 26 Mar 2026 - 6:21

score 38 · Answer 9 · 2018-05-19 23:16:18

38

Views

How is the formula for expressing a cyclotomic polynomial derived.

Published on 19 May 2018 - 23:16

score 38 · Answer 10 · 2026-03-25 11:27:16

38

Views

Is there a more elegant method to prove that we are in need of a field extension than the one I use?

Published on 25 Mar 2026 - 11:27

score 122 · Answer 11 · 2026-03-26 06:21:35

122

Views

Roots of $x^8-3$ over $GF(17)$

Published on 26 Mar 2026 - 6:21

score 196 · Answer 12 · 2026-03-25 12:27:21

196

Views

what's the most efficient way to find the minimal polynomial of a matrix?

Published on 25 Mar 2026 - 12:27

score 354 · Answer 13 · 2026-03-25 10:59:00

354

Views

A quotient of a product of prime characteristic fields is isomorphic to a subfield of $\mathbf{C}$

Published on 25 Mar 2026 - 10:59

score 61 · Answer 14 · 2026-03-27 23:40:36

61

Views

$E/K$ is finite Galois extension. Let $G(E/K)=\{\sigma_i\}$ be its Galois group. Then $\sigma_i$ are linearly independent over $E$?

Published on 27 Mar 2026 - 23:40

score 184 · Answer 15 · 2026-03-27 12:00:30

184

Views

Decomposable Modules

Published on 27 Mar 2026 - 12:00

List Question

Find $G (K/F) $ where $K $ is a splitting field of $t^p-t-a \in F [t] $.

In a Galois group of $F(a_1,...,a_n)/F $ with $a_i$'s algebraic, where does the $a_i $'s get mapped to

Let $\alpha=\sqrt[5]{2}+\sqrt{5}$, show that $\sqrt{5}\in\mathbb{Q}(\alpha)$.

Epimorphism, in the category of commutative rings with unity , with domain a field is an isomorphism?

Let $F/K,F'/K'$ be two galois extensions(maybe infinite), $F\subset F',K\subset K'$, is $G(F'/K')\to G(F/K)$ via restriction open map?

If $K $ is infinite and $u,v $ are separable and algebraic over $K $ then there is some $a \in K $ such that $K (u+av)=K (u,v) $ proof verification

Minimal polynomial of $\alpha+i$ over $\mathbb{Q}$

How many subfields of order $p^m$ in $\mathbb{F}_{p^n}$

How is the formula for expressing a cyclotomic polynomial derived.

Is there a more elegant method to prove that we are in need of a field extension than the one I use?

Roots of $x^8-3$ over $GF(17)$

what's the most efficient way to find the minimal polynomial of a matrix?

A quotient of a product of prime characteristic fields is isomorphic to a subfield of $\mathbf{C}$

$E/K$ is finite Galois extension. Let $G(E/K)=\{\sigma_i\}$ be its Galois group. Then $\sigma_i$ are linearly independent over $E$?

Decomposable Modules

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