Question

Degree of a separable extension of a Dedekind ring's quotient field

score 121 · Answer 1 · 2022-09-15 13:11:54

121

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Degree of a separable extension of a Dedekind ring's quotient field

Published on 15 Sep 2022 - 13:11

score 531 · Answer 2 · 2022-09-18 16:24:47

531

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Show $\alpha$ is separable over a field $F$ iff $F(\alpha) = F(\alpha^p)$.

Published on 18 Sep 2022 - 16:24

score 151 · Answer 3 · 2022-09-20 16:31:55

151

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Question about what is a separable polynomial

Published on 20 Sep 2022 - 16:31

score 86 · Answer 4 · 2022-09-26 20:13:10

86

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Why is an element separable only if it is of the form $\alpha^p$ for some $\alpha$?

Published on 26 Sep 2022 - 20:13

score 83 · Answer 5 · 2022-09-27 05:43:27

83

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A field extension is separable iff it is contained in a Galois Extension

Published on 27 Sep 2022 - 5:43

score 25 · Answer 6 · 2022-09-29 22:54:29

25

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Are inseparable elements of an extension field closed under addition?

Published on 29 Sep 2022 - 22:54

score 32 · Answer 7 · 2022-10-03 15:27:31

32

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Why do two minimal polynomials of $\alpha$ over different extensions share the multiplicity of $\alpha$?

Published on 03 Oct 2022 - 15:27

score 106 · Answer 8 · 2022-10-03 18:02:44

106

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When is the product of two separable polynomials necessarily separable?

Published on 03 Oct 2022 - 18:02

score 58 · Answer 9 · 2022-10-08 06:48:45

58

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Finding the roots of $x^5-2$. My question is about finding the $5^{th}$ roots of 2.While the associated question is about finding roots of unity

Published on 08 Oct 2022 - 6:48

score 95 · Answer 10 · 2022-10-11 19:39:47

95

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Infinite algebraic field extension of a finite field is normal and separable

Published on 11 Oct 2022 - 19:39

score 64 · Answer 11 · 2022-10-24 09:21:25

64

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Why is $K^{\mathrm{sep}}$ dense in $K_v^{\mathrm{sep}}$?

Published on 24 Oct 2022 - 9:21

score 25 · Answer 12 · 2022-11-02 11:13:32

25

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Proving the Existence of an Intermediate Field with Special Properties in an Inseparable Field Extension

Published on 02 Nov 2022 - 11:13

score 56 · Answer 13 · 2022-11-06 17:23:33

56

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Composition of two simple field extension with coprime degree is simple?

Published on 06 Nov 2022 - 17:23

score 318 · Answer 14 · 2022-11-20 00:52:45

318

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Why is a field extension separable if and only if the discriminant of the basis of the field extension is nonzero?

Published on 20 Nov 2022 - 0:52

score 47 · Answer 15 · 2022-12-06 04:26:02

47

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Question about the minimal polynomial of an inseparable element in a field

Published on 06 Dec 2022 - 4:26

List Question

Degree of a separable extension of a Dedekind ring's quotient field

Show $\alpha$ is separable over a field $F$ iff $F(\alpha) = F(\alpha^p)$.

Question about what is a separable polynomial

Why is an element separable only if it is of the form $\alpha^p$ for some $\alpha$?

A field extension is separable iff it is contained in a Galois Extension

Are inseparable elements of an extension field closed under addition?

Why do two minimal polynomials of $\alpha$ over different extensions share the multiplicity of $\alpha$?

When is the product of two separable polynomials necessarily separable?

Finding the roots of $x^5-2$. My question is about finding the $5^{th}$ roots of 2.While the associated question is about finding roots of unity

Infinite algebraic field extension of a finite field is normal and separable

Why is $K^{\mathrm{sep}}$ dense in $K_v^{\mathrm{sep}}$?

Proving the Existence of an Intermediate Field with Special Properties in an Inseparable Field Extension

Composition of two simple field extension with coprime degree is simple?

Why is a field extension separable if and only if the discriminant of the basis of the field extension is nonzero?

Question about the minimal polynomial of an inseparable element in a field

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