List questions from splitting-field

Published on 29 Mar 2026 - 19:11

255

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Question in proof of the existence of a field of order $p^n$

Published on 19 Apr 2021 - 22:22

132

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Show that any degree $k$ polynomial divides $e_q=x^q-x$ with $q=p^{km}$ in $\mathbb Z_p$.

Published on 25 Apr 2021 - 4:29

24

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A question related to intermediate fields

Published on 26 Apr 2021 - 17:06

53

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Is this definition of splitting field pleonastic?

Published on 28 Apr 2021 - 13:04

75

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What does it mean when one talks about splitting field of a multivariable polynomial? And then, Galois group of that splitting field?

Published on 30 Mar 2026 - 7:09

61

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A Field Contained in All Fields

Published on 29 Apr 2021 - 4:01

73

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Question on proof of Theorem 24.8 of Abstract Algebra by Saracino

Published on 29 Apr 2021 - 20:26

65

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Proving the irreducibility of a polynomial based on its Galois group

Published on 30 Mar 2026 - 7:09

57

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Extension of a field monomorphism to an automorphism .

Published on 02 May 2021 - 22:35

371

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Prove this $\mathbb F_2 (a)$ is splitting field of $X^4+X+1$

Published on 03 May 2021 - 6:46

88

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Splitting Field of $x^4−2x^2−2$

Published on 08 May 2021 - 4:09

42

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Compute certain $Aut_{\mathbb Q}(L)$

Published on 01 Apr 2026 - 3:01

102

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Splitting field over the field of fractions $\mathbb{Z}_p(x)$

Published on 09 May 2021 - 2:23

127

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Galois extension: does isomorphism in subgroups implies isomorphism of the subfield?

Published on 09 May 2021 - 4:59

List Question

Reconstructing a polynomial's Galois group from those of its subfield factors

Question in proof of the existence of a field of order $p^n$

Show that any degree $k$ polynomial divides $e_q=x^q-x$ with $q=p^{km}$ in $\mathbb Z_p$.

A question related to intermediate fields

Is this definition of splitting field pleonastic?

What does it mean when one talks about splitting field of a multivariable polynomial? And then, Galois group of that splitting field?

A Field Contained in All Fields

Question on proof of Theorem 24.8 of Abstract Algebra by Saracino

Proving the irreducibility of a polynomial based on its Galois group

Extension of a field monomorphism to an automorphism .

Prove this $\mathbb F_2 (a)$ is splitting field of $X^4+X+1$

Splitting Field of $x^4−2x^2−2$

Compute certain $Aut_{\mathbb Q}(L)$

Splitting field over the field of fractions $\mathbb{Z}_p(x)$

Galois extension: does isomorphism in subgroups implies isomorphism of the subfield?

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