List questions from field-theory

Published on 27 Mar 2026 - 13:24

180

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Is there a converse of Abhyankar-Moh-Suzuki theorem?

Published on 02 Jul 2018 - 5:37

88

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Let $l:=\text{lcm}(n,m)$. Show $\mathbb Q(\zeta_n,\zeta_m)=\mathbb Q(\zeta_l)$.

Published on 24 Mar 2026 - 22:07

222

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The Algebraic dependence of two rational functions

Published on 02 Jul 2018 - 18:23

792

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Galois group and intermediate subfields of finite field extension

Published on 25 Mar 2026 - 13:13

42

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Caracterization of algebraic extensions

Published on 28 Mar 2026 - 15:20

48

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Ideals in Commutative Rings Containing a Field

Published on 25 Mar 2026 - 23:07

106

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Does the existence of the field element $-0_F$ in the field $F$ follow from the existence of the additive inverse?

Published on 03 Jul 2018 - 23:43

244

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Defining $\mathbb{C}$ without defining $\mathbb{R}$

Published on 04 Jul 2018 - 3:18

170

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Fastest way to factorize $x^{18}-x^3$ over $\mathbb{F}_2$

Published on 25 Mar 2026 - 12:53

62

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Some proofs for Cyclotomic extension $\Bbb K(\xi _n)/ \Bbb K $

Published on 28 Mar 2026 - 20:55

62

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The Galois group corresponded to a polynomial of 5 degree

Published on 28 Mar 2026 - 16:58

53

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Is every finite dimensional field extension a matrix algebra?

Published on 28 Mar 2026 - 20:54

51

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Exercise about the form of elements of $\mathbb{Q}(u)$

Published on 29 Mar 2026 - 17:26

810

Views

Factorize $x^8-x$ over $F_3$ and $F_{81}$

Published on 25 Mar 2026 - 14:33

List Question

when can I get a Galois element from the permutation of the roots?

Is there a converse of Abhyankar-Moh-Suzuki theorem?

Let $l:=\text{lcm}(n,m)$. Show $\mathbb Q(\zeta_n,\zeta_m)=\mathbb Q(\zeta_l)$.

The Algebraic dependence of two rational functions

Galois group and intermediate subfields of finite field extension

Caracterization of algebraic extensions

Ideals in Commutative Rings Containing a Field

Does the existence of the field element $-0_F$ in the field $F$ follow from the existence of the additive inverse?

Defining $\mathbb{C}$ without defining $\mathbb{R}$

Fastest way to factorize $x^{18}-x^3$ over $\mathbb{F}_2$

Some proofs for Cyclotomic extension $\Bbb K(\xi _n)/ \Bbb K $

The Galois group corresponded to a polynomial of 5 degree

Is every finite dimensional field extension a matrix algebra?

Exercise about the form of elements of $\mathbb{Q}(u)$

Factorize $x^8-x$ over $F_3$ and $F_{81}$

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