List questions from extension-field

Published on 14 Apr 2026 - 12:29

76

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Deriving the addition and product on $\mathbb C$

Published on 16 Apr 2026 - 17:11

26

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Degree of inseparable subfields of a matrix algebra

Published on 11 Apr 2026 - 5:03

39

Views

Constructing an algebraically closed extension-field of an already algebraically closed field

Published on 15 Apr 2026 - 19:12

219

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Show that $[\mathbb{Z}_p(x,y):\mathbb{Z}_p(x^p,y^p)]=p^2$ and that $\mathbb{Z}_p(x,y)$ is not a simple extension of $\mathbb{Z}_p(x^p,y^p)$

Published on 15 Apr 2026 - 3:57

30

Views

Show that $[K(a) : K] \leq [F(a) : F]$

Published on 16 Apr 2026 - 5:07

35

Views

Question about purely transcendental extension

Published on 26 Mar 2026 - 14:33

63

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Show that $\{1,x,x^2\}$ is $\mathbb{Q}-$base of $\mathbb{Q}(x)$

Published on 17 Apr 2026 - 2:54

41

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Prove that $\mathbb{Q}(y) \in \{\mathbb{Q},\mathbb{Q}(x)\}$

Published on 17 Apr 2026 - 0:32

38

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Understanding proof with isomorphic field of fractions

Published on 09 Apr 2026 - 1:25

61

Views

Maps from field extensions of $\mathbb{Q}$ to $\mathbb{C}$

Published on 16 Apr 2026 - 18:39

79

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Basis of $\mathbb{Q}(i\sqrt{2},\sqrt{3},\beta)/\mathbb{Q}$, being $\beta$ root of $x^3+5x-3$

Published on 16 Apr 2026 - 17:01

59

Views

Constructing an algebraic extension of degree n of $\mathbb{Z}_p$

Published on 13 Apr 2026 - 19:46

113

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Show that $\alpha(a)$ is also a root of $f(x)$

Published on 14 Apr 2026 - 7:01

86

Views

Integral basis for totally ramified extensions of $p$-adic fields

Published on 16 Apr 2026 - 10:52

List Question

What would be the image of $1+\pi O_K$ under the field norm?

Deriving the addition and product on $\mathbb C$

Degree of inseparable subfields of a matrix algebra

Constructing an algebraically closed extension-field of an already algebraically closed field

Show that $[\mathbb{Z}_p(x,y):\mathbb{Z}_p(x^p,y^p)]=p^2$ and that $\mathbb{Z}_p(x,y)$ is not a simple extension of $\mathbb{Z}_p(x^p,y^p)$

Show that $[K(a) : K] \leq [F(a) : F]$

Question about purely transcendental extension

Show that $\{1,x,x^2\}$ is $\mathbb{Q}-$base of $\mathbb{Q}(x)$

Prove that $\mathbb{Q}(y) \in \{\mathbb{Q},\mathbb{Q}(x)\}$

Understanding proof with isomorphic field of fractions

Maps from field extensions of $\mathbb{Q}$ to $\mathbb{C}$

Basis of $\mathbb{Q}(i\sqrt{2},\sqrt{3},\beta)/\mathbb{Q}$, being $\beta$ root of $x^3+5x-3$

Constructing an algebraic extension of degree n of $\mathbb{Z}_p$

Show that $\alpha(a)$ is also a root of $f(x)$

Integral basis for totally ramified extensions of $p$-adic fields

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