List questions from field-theory

Published on 27 Mar 2026 - 10:15

47

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Is it necessary to say $x$ is an integral element of $L$?

Published on 29 Mar 2026 - 18:14

134

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Field lines of a vector field

Published on 28 Mar 2026 - 20:13

81

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Dependent Column Vectors iff Zero Determinant for any Field?

Published on 28 Mar 2026 - 17:39

266

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Is the compositum of two finite field extensions finite?

Published on 29 Mar 2026 - 18:14

246

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Infinitely many number fields

Published on 27 Mar 2026 - 16:19

105

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Show that $\Bbb Z_p[i]$ is isomorphic to $\Bbb Z_p[x]/\langle x^2+1\rangle$.

Published on 23 Mar 2026 - 12:17

356

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If $L:K$ is a radical extension in $\mathbb {C}$, then the normal closure $M:K$ of $L:K$ is also radical.

Published on 29 Mar 2026 - 22:29

571

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Find the smallest normal extension (upto isomorphism) of $\Bbb{Q}(2^{1/4}, 3^{1/4})$ in $\overline{\Bbb{Q}}.$

Published on 25 Mar 2026 - 16:13

72

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Extension of a $F$-homomorphism where $F$ is a field.

Published on 29 Mar 2026 - 18:15

157

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Correct interpretation of solubility by radicals.

Published on 29 Mar 2026 - 22:34

45

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Separable Functions and Derivatives

Published on 25 Oct 2018 - 17:21

37

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Let $f(x)\in F[x]$, degree$(f(x))=n>1$, char$(F)=p$, prime and $f'(x)=0$. Prove, $p\mid n$ and $f(x)$ has at most $n/p$ distinct roots.

Published on 29 Mar 2026 - 18:18

164

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Is any rational extension of degree 3 of the form $\mathbb{Q}(\sqrt[3]{d})$?

Published on 25 Mar 2026 - 9:10

329

Views

Use Artin's Theorem to show that $[E:k] \ge n$

Published on 27 Oct 2018 - 3:22

List Question

Existence of certain autormorphism in Normal extensions

Is it necessary to say $x$ is an integral element of $L$?

Field lines of a vector field

Dependent Column Vectors iff Zero Determinant for any Field?

Is the compositum of two finite field extensions finite?

Infinitely many number fields

Show that $\Bbb Z_p[i]$ is isomorphic to $\Bbb Z_p[x]/\langle x^2+1\rangle$.

If $L:K$ is a radical extension in $\mathbb {C}$, then the normal closure $M:K$ of $L:K$ is also radical.

Find the smallest normal extension (upto isomorphism) of $\Bbb{Q}(2^{1/4}, 3^{1/4})$ in $\overline{\Bbb{Q}}.$

Extension of a $F$-homomorphism where $F$ is a field.

Correct interpretation of solubility by radicals.

Separable Functions and Derivatives

Let $f(x)\in F[x]$, degree$(f(x))=n>1$, char$(F)=p$, prime and $f'(x)=0$. Prove, $p\mid n$ and $f(x)$ has at most $n/p$ distinct roots.

Is any rational extension of degree 3 of the form $\mathbb{Q}(\sqrt[3]{d})$?

Use Artin's Theorem to show that $[E:k] \ge n$

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