List questions from extension-field

Published on 15 Apr 2026 - 13:52

119

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Showing that every polynomial over the Algebraic Numbers has a $0$ in the Algebraic Numbers.

Published on 13 Apr 2026 - 2:52

61

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Potentially diagonal $K$-algebra

Published on 15 Apr 2026 - 5:10

147

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Transcendental extension not isomorphic to its closure

Published on 15 Apr 2026 - 8:47

2.2k

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Roots of polynomial in field extension

Published on 15 Apr 2026 - 14:33

44

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What are the submodules of $M⊗K$?

Published on 10 Apr 2026 - 17:28

611

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Closeness of field extensions under complex conjugation

Published on 12 Apr 2026 - 19:34

2.2k

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Let $F=\mathbf Z_2$ and let $f(x)=x^3+x+1 \in F[x]$ and let a be a zero of $f(x)$ in some extension of $F$

Published on 16 Apr 2026 - 0:54

263

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A field extension K/F is biquadratic if [K:F] = 4 and if $K$ is generated by the roots of two irreducible quadratic polynomials

Published on 15 Apr 2026 - 18:45

1.4k

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How many quadratic extension are there on a field?

Published on 13 Apr 2026 - 3:49

161

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How many fields are there between $\mathbb{Q}$ and $\mathbb{Q}(\zeta_{15})$?

Published on 29 Mar 2026 - 17:31

1.8k

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Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$

Published on 12 Apr 2026 - 9:06

139

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$L$ is Galois and $a \in K \implies L=K(\sqrt{a})$

Published on 14 Apr 2026 - 8:11

67

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Nonisomorphic field extensions in which a polynomial has a root

Published on 12 Apr 2026 - 6:27

82

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How to describe the field extension?

Published on 10 Apr 2026 - 7:38

List Question

Cyclic extension of degree $2$ of $\mathbb{F_2}$

Showing that every polynomial over the Algebraic Numbers has a $0$ in the Algebraic Numbers.

Potentially diagonal $K$-algebra

Transcendental extension not isomorphic to its closure

Roots of polynomial in field extension

What are the submodules of $M⊗K$?

Closeness of field extensions under complex conjugation

Let $F=\mathbf Z_2$ and let $f(x)=x^3+x+1 \in F[x]$ and let a be a zero of $f(x)$ in some extension of $F$

A field extension K/F is biquadratic if [K:F] = 4 and if $K$ is generated by the roots of two irreducible quadratic polynomials

How many quadratic extension are there on a field?

How many fields are there between $\mathbb{Q}$ and $\mathbb{Q}(\zeta_{15})$?

Show that $\mathbb{Q}(\zeta_n)$ is Galois over $\mathbb{Q}$ and $Gal(\mathbb{Q}(\zeta_n)/\mathbb{Q}))\cong \mathbb{Z_n}^*$

$L$ is Galois and $a \in K \implies L=K(\sqrt{a})$

Nonisomorphic field extensions in which a polynomial has a root

How to describe the field extension?

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