Question

Let $L/K$ be a purely inseparable extension of degree $p$. Prove that $L=K(\alpha)$ for some $\alpha \in L.$

score 61 · Answer 1 · 2026-04-12 23:59:49

61

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Let $L/K$ be a purely inseparable extension of degree $p$. Prove that $L=K(\alpha)$ for some $\alpha \in L.$

Published on 12 Apr 2026 - 23:59

score 88 · Answer 2 · 2026-04-16 00:29:15

88

Views

Prove check: $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational using field extension

Published on 16 Apr 2026 - 0:29

score 33 · Answer 3 · 2026-04-13 07:18:08

33

Views

Is there any criterion for a number field whose every embedding to $\mathbb{C}$ is closed under complex conjugate?

Published on 13 Apr 2026 - 7:18

score 46 · Answer 4 · 2026-04-14 08:02:16

46

Views

Proving without derivative that extension of a characteristic zero field is separable

Published on 14 Apr 2026 - 8:02

score 57 · Answer 5 · 2026-04-11 20:46:09

57

Views

Galois group of an arbitrary field extension

Published on 11 Apr 2026 - 20:46

score 102 · Answer 6 · 2026-04-14 15:07:04

102

Views

Subfield Lattice for $\mathbb Q(\zeta_{16})$

Published on 14 Apr 2026 - 15:07

score 59 · Answer 7 · 2026-04-24 03:48:48

59

Views

Number of polynomials with distinct roots.

Published on 24 Apr 2026 - 3:48

score 291 · Answer 8 · 2026-04-09 02:23:24

291

Views

the definition of field in mathematics

Published on 09 Apr 2026 - 2:23

score 83 · Answer 9 · 2026-04-16 00:20:02

83

Views

Extension degree of the minimal splitting field of $X^4+2tX^2+t$ over $\mathbb{C}(t)$

Published on 16 Apr 2026 - 0:20

score 54 · Answer 10 · 2026-04-13 08:29:42

54

Views

Group superscript on field

Published on 13 Apr 2026 - 8:29

score 113 · Answer 11 · 2026-04-15 15:22:00

113

Views

How do we find the conjugates of a field element over $GF[2^{4}]$? And why can we take the LCM of just odd-indexed min.polynomials for g(x)?

Published on 15 Apr 2026 - 15:22

score 87 · Answer 12 · 2026-04-14 03:04:41

87

Views

How to interpret number theory result in the language of groups rings and fields?

Published on 14 Apr 2026 - 3:04

score 51 · Answer 13 · 2026-04-13 12:45:07

51

Views

How to find the zeroes of a BCH code and how do they define the dimensions of a parity check matrix?

Published on 13 Apr 2026 - 12:45

score 147 · Answer 14 · 2026-04-15 00:56:45

147

Views

Galois group for splitting field of $\sqrt[3]{2+\sqrt2}$ and $\sqrt{2+\sqrt[3]2}$

Published on 15 Apr 2026 - 0:56

score 26 · Answer 15 · 2026-04-17 12:18:27

$ev_{\alpha}: K[x]\to K$ is $g(x)\mapsto g(\alpha)$, then $ker(ev_{\alpha})$ is a nonzero prime ideal iff $K[\alpha]=ev_{\alpha}(K[x])$ is a field.

List Question

Let $L/K$ be a purely inseparable extension of degree $p$. Prove that $L=K(\alpha)$ for some $\alpha \in L.$

Prove check: $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational using field extension

Is there any criterion for a number field whose every embedding to $\mathbb{C}$ is closed under complex conjugate?

Proving without derivative that extension of a characteristic zero field is separable

Galois group of an arbitrary field extension

Subfield Lattice for $\mathbb Q(\zeta_{16})$

Number of polynomials with distinct roots.

the definition of field in mathematics

Extension degree of the minimal splitting field of $X^4+2tX^2+t$ over $\mathbb{C}(t)$

Group superscript on field

How do we find the conjugates of a field element over $GF[2^{4}]$? And why can we take the LCM of just odd-indexed min.polynomials for g(x)?

How to interpret number theory result in the language of groups rings and fields?

How to find the zeroes of a BCH code and how do they define the dimensions of a parity check matrix?

Galois group for splitting field of $\sqrt[3]{2+\sqrt2}$ and $\sqrt{2+\sqrt[3]2}$

$ev_{\alpha}: K[x]\to K$ is $g(x)\mapsto g(\alpha)$, then $ker(ev_{\alpha})$ is a nonzero prime ideal iff $K[\alpha]=ev_{\alpha}(K[x])$ is a field.

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