List questions from extension-field

Published on 12 Apr 2026 - 8:01

175

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$\mathbb{Q}(\omega2^{1/3}) \neq \mathbb{Q}(\omega^{2}2^{1/3})$

Published on 16 Apr 2026 - 14:59

77

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p-th powers in $\mathbb{Q}_p(\zeta)$

Published on 12 Apr 2026 - 17:29

57

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For $\omega=e^{2\pi i/q}$ and $c_0,\ldots,c_{q-1}\in \mathbb Z$, $\sum\limits_{k=0}^{q-1}c_k\omega^k \equiv \sum\limits_{k=0}^{q-1}c_k\pmod p$.

Published on 15 Apr 2026 - 11:37

172

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Unit in abelian extension of rationals

Published on 16 Apr 2026 - 10:57

93

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Integral closure of UFD in extension field of degree 2

Published on 12 Apr 2026 - 21:01

183

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Irreducible polynomial over normal extension

Published on 14 Apr 2026 - 4:39

51

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Are these two fields $\mathbb {F}_{p}(x)$ and $\mathbb {F}_{p}(x^p)$ are isomorphic fields?

Published on 16 Apr 2026 - 22:30

571

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Example of extension $\mathbb{Q}(a,b) / \mathbb{Q}$ that is not simple? And more.

Published on 16 Apr 2026 - 2:03

67

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Extending $\mathbb Q$ with different roots of $x^5-15$ results in different fields.

Published on 13 Apr 2026 - 9:40

59

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Let $K=F(\frac{x^7}{x^5+x^3+3x+1})$, where $F$ is a field. Determine $[F(x): K]$.

Published on 17 Apr 2026 - 11:03

208

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Galois group of $x^5-5x^3+4x+1 \in \mathbb{Q}[x] $

Published on 16 Apr 2026 - 8:49

42

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$E=F[\alpha]$, where $\alpha$ is a root of $x^p-x-c$.

Published on 16 Apr 2026 - 22:43

242

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Let $K$ be an extension field of $F$ and let $a$ be an element of $K$. Show that if $F(a)=F(a^2)$, then $a$ is algebraic over $F$.

Published on 16 Apr 2026 - 14:50

73

Views

A theoretical idea for proof of a theorem of field extension

Published on 09 Apr 2026 - 16:25

List Question

Extension field: a question about algebric extension field

$\mathbb{Q}(\omega2^{1/3}) \neq \mathbb{Q}(\omega^{2}2^{1/3})$

p-th powers in $\mathbb{Q}_p(\zeta)$

For $\omega=e^{2\pi i/q}$ and $c_0,\ldots,c_{q-1}\in \mathbb Z$, $\sum\limits_{k=0}^{q-1}c_k\omega^k \equiv \sum\limits_{k=0}^{q-1}c_k\pmod p$.

Unit in abelian extension of rationals

Integral closure of UFD in extension field of degree 2

Irreducible polynomial over normal extension

Are these two fields $\mathbb {F}_{p}(x)$ and $\mathbb {F}_{p}(x^p)$ are isomorphic fields?

Example of extension $\mathbb{Q}(a,b) / \mathbb{Q}$ that is not simple? And more.

Extending $\mathbb Q$ with different roots of $x^5-15$ results in different fields.

Let $K=F(\frac{x^7}{x^5+x^3+3x+1})$, where $F$ is a field. Determine $[F(x): K]$.

Galois group of $x^5-5x^3+4x+1 \in \mathbb{Q}[x] $

$E=F[\alpha]$, where $\alpha$ is a root of $x^p-x-c$.

Let $K$ be an extension field of $F$ and let $a$ be an element of $K$. Show that if $F(a)=F(a^2)$, then $a$ is algebraic over $F$.

A theoretical idea for proof of a theorem of field extension

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