List questions from field-theory

Published on 12 Apr 2026 - 19:06

365

Views

Isomorphism of Extensions

Published on 13 Apr 2026 - 2:36

70

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Show that $\mathbb{F}_{2^2}=\mathbb{Z}_2(a)$

Published on 16 Apr 2026 - 15:35

159

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Field Extensions and Number of Isomorphisms

Published on 10 Apr 2026 - 21:43

159

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$\{p_i\}$ generate the $k$-algebra of symmetric polynomials in $k[t_1, \dots, t_n]$ and are algebraically independent over $k$

Published on 17 May 2026 - 1:26

66

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Normal soluble field towers

Published on 14 Apr 2026 - 5:57

62

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Show that the intersection is $F$

Published on 15 Apr 2026 - 3:58

90

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Finite fields and order

Published on 16 Apr 2026 - 22:58

106

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$G$ is isomorphic to $S_3$

Published on 16 Apr 2026 - 14:46

95

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$X$ is algebraic over $E$

Published on 12 Apr 2026 - 0:59

282

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The polynomial splits into distinct factors in $F[x]$

Published on 13 Apr 2026 - 13:11

114

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What is the splitting field of $t^4+2$?

Published on 16 Apr 2026 - 21:28

87

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If an irreducible $f(x)$ divides $f(x^2)$, then its splitting field is $F(\alpha)$ for any root $\alpha$ of $f(x)$?

Published on 16 Apr 2026 - 0:22

46

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The equation has a solution iff $(k,q-1)=1$

Published on 14 Apr 2026 - 18:11

51

Views

Show that it is an element of $L$

Published on 13 Apr 2026 - 7:34

List Question

Orbits of elements of the field under the action of a subgroup of field automorphisms

Isomorphism of Extensions

Show that $\mathbb{F}_{2^2}=\mathbb{Z}_2(a)$

Field Extensions and Number of Isomorphisms

$\{p_i\}$ generate the $k$-algebra of symmetric polynomials in $k[t_1, \dots, t_n]$ and are algebraically independent over $k$

Normal soluble field towers

Show that the intersection is $F$

Finite fields and order

$G$ is isomorphic to $S_3$

$X$ is algebraic over $E$

The polynomial splits into distinct factors in $F[x]$

What is the splitting field of $t^4+2$?

If an irreducible $f(x)$ divides $f(x^2)$, then its splitting field is $F(\alpha)$ for any root $\alpha$ of $f(x)$?

The equation has a solution iff $(k,q-1)=1$

Show that it is an element of $L$

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