Question

How to find the smallest extension field of $GF(p)$ which is a splitting field for all quotient groups $N_i/P_i$?

score 33 · Answer 1 · 2026-03-28 09:28:38

33

Views

How to find the smallest extension field of $GF(p)$ which is a splitting field for all quotient groups $N_i/P_i$?

Published on 28 Mar 2026 - 9:28

score 90 · Answer 2 · 2019-03-09 22:51:40

90

Views

Let $F$ be a field. Is it true that if $[F(\sqrt{D}) : F] = 2$, then $D \in F$?

Published on 09 Mar 2019 - 22:51

score 145 · Answer 3 · 2026-03-25 17:21:31

145

Views

Found $x^8$ while calculating inverse of $(x^6+1)$ in finite field $GF(2^8)$. Help???

Published on 25 Mar 2026 - 17:21

score 71 · Answer 4 · 2019-03-11 22:08:06

71

Views

Question about a Simple Field Extensions Equality

Published on 11 Mar 2019 - 22:08

score 19 · Answer 5 · 2019-03-12 13:51:09

19

Views

Series of Extension Fields

Published on 12 Mar 2019 - 13:51

score 54 · Answer 6 · 2026-03-28 12:39:22

54

Views

Kernel is a group of order $q+1$

Published on 28 Mar 2026 - 12:39

score 111 · Answer 7 · 2026-03-25 23:56:34

111

Views

Extension of Splitting Fields over An Arbitrary Field

Published on 25 Mar 2026 - 23:56

score 964 · Answer 8 · 2026-03-25 17:26:52

964

Views

If $u\in F$ is Transcendental over $K$, $F$ an extension field of $K$, Show every element in $K(u)$ not in $K$ is transcendental over $K$.

Published on 25 Mar 2026 - 17:26

score 315 · Answer 9 · 2019-03-17 07:58:15

315

Views

Prove that $\Bbb Q(\sqrt{2},3^{1/3})=\Bbb Q(\sqrt{2}+3^{1/3})$

Published on 17 Mar 2019 - 7:58

score 839 · Answer 10 · 2026-03-27 23:20:10

839

Views

Is the extension $\mathbb{Q}(\sqrt{5},\sqrt{7})$ simple? If so/not, why?

Published on 27 Mar 2026 - 23:20

score 90 · Answer 11 · 2019-03-17 23:53:25

Let $L/K$ be a field extension and let $a, b \in L$ be algebraic elements over $K$ having the same minimal polynomial. Show that $K(a) \simeq K(b)$.

score 33 · Answer 12 · 2019-03-18 07:32:13

33

Views

A generator of a different form than the one given by the primitive element theorem

Published on 18 Mar 2019 - 7:32

score 59 · Answer 13 · 2019-03-18 15:43:03

59

Views

Let $K$ be an extension of a field $F$ such that $[K:F] = 13$.Suppose $a$ $∈$ $K-F$.What is the value of $[F(a):F] $?

Published on 18 Mar 2019 - 15:43

score 72 · Answer 14 · 2019-03-19 00:15:07

72

Views

How is an arbitrary member of $\mathbb{Q}(\pi)$ defined?

Published on 19 Mar 2019 - 0:15

score 202 · Answer 15 · 2026-03-25 04:38:28

202

Views

Quadratic Fields and Gauss Sums

Published on 25 Mar 2026 - 4:38

List Question

How to find the smallest extension field of $GF(p)$ which is a splitting field for all quotient groups $N_i/P_i$?

Let $F$ be a field. Is it true that if $[F(\sqrt{D}) : F] = 2$, then $D \in F$?

Found $x^8$ while calculating inverse of $(x^6+1)$ in finite field $GF(2^8)$. Help???

Question about a Simple Field Extensions Equality

Series of Extension Fields

Kernel is a group of order $q+1$

Extension of Splitting Fields over An Arbitrary Field

If $u\in F$ is Transcendental over $K$, $F$ an extension field of $K$, Show every element in $K(u)$ not in $K$ is transcendental over $K$.

Prove that $\Bbb Q(\sqrt{2},3^{1/3})=\Bbb Q(\sqrt{2}+3^{1/3})$

Is the extension $\mathbb{Q}(\sqrt{5},\sqrt{7})$ simple? If so/not, why?

Let $L/K$ be a field extension and let $a, b \in L$ be algebraic elements over $K$ having the same minimal polynomial. Show that $K(a) \simeq K(b)$.

A generator of a different form than the one given by the primitive element theorem

Let $K$ be an extension of a field $F$ such that $[K:F] = 13$.Suppose $a$ $∈$ $K-F$.What is the value of $[F(a):F] $?

How is an arbitrary member of $\mathbb{Q}(\pi)$ defined?

Quadratic Fields and Gauss Sums

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