Question

If $f=\prod_{k=1}^m f_k$ in $L[X]$ show that there is an automorphism in $L$ such that $f_k^{\sigma }=f_j$

score 36 · Answer 1 · 2026-04-16 11:47:50

36

Views

If $f=\prod_{k=1}^m f_k$ in $L[X]$ show that there is an automorphism in $L$ such that $f_k^{\sigma }=f_j$

Published on 16 Apr 2026 - 11:47

score 86 · Answer 2 · 2026-04-16 23:16:35

86

Views

Degree and Galois group of $\mathbb{Q}(\sqrt[3]{2},\sqrt{-3})/\mathbb{Q}(\sqrt{-3})$.

Published on 16 Apr 2026 - 23:16

score 91 · Answer 3 · 2026-04-15 22:26:45

91

Views

All roots of $X^{p^r}-a$ are equal?

Published on 15 Apr 2026 - 22:26

score 81 · Answer 4 · 2026-04-16 17:22:00

81

Views

Factorization of $x^3-10x+4$ over $\mathbb Q(\sqrt 2, \sqrt[3] 2)$

Published on 16 Apr 2026 - 17:22

score 36 · Answer 5 · 2026-04-12 09:06:01

36

Views

Question about the proof of: $E/k$ is algebraic of characteristic zero. Every $f(x)\in k[x]$ has a root in $E$. Then $E$ is algebraically closed.

Published on 12 Apr 2026 - 9:06

score 61 · Answer 6 · 2026-04-15 10:53:16

61

Views

Are $\mathbb{C}(x)\otimes_\mathbb{R}\mathbb{C}(y)$ and $\mathbb{C}(x)\otimes_\mathbb{C}\mathbb{C}(y)$ integral domains or fields?

Published on 15 Apr 2026 - 10:53

score 224 · Answer 7 · 2026-05-11 09:35:38

224

Views

Does there exist a Cauchy-complete, non-Archimedean ordered field that is not isomorphic to a field extension of $\mathbb{R}$?

Published on 11 May 2026 - 9:35

score 52 · Answer 8 · 2026-04-16 04:52:04

52

Views

Generalizations of Algebraic Closures

Published on 16 Apr 2026 - 4:52

score 94 · Answer 9 · 2026-04-16 21:52:11

94

Views

necessary and sufficient conditions so that $\mathbb{Q}(\alpha)$ and $\mathbb{Q}(\beta)$ are isomorphic

Published on 16 Apr 2026 - 21:52

score 78 · Answer 10 · 2026-04-17 13:46:45

78

Views

Prove there is no field F satisfying R ⊊ F ⊊ C

Published on 17 Apr 2026 - 13:46

score 188 · Answer 11 · 2026-04-16 07:22:28

188

Views

If $a^n = a$ for all $a \in K$, what is $\operatorname{char} K$?

Published on 16 Apr 2026 - 7:22

score 96 · Answer 12 · 2026-04-16 11:51:34

96

Views

Suppose $B$ lies over $A$, s.t. $A,B$ integral domains. Does this tell us anything about which homomorphisms from $A$ to a field we can extend to $B$?

Published on 16 Apr 2026 - 11:51

score 52 · Answer 13 · 2026-04-10 02:37:38

52

Views

Natural irrationalities for infinite Galois extensions

Published on 10 Apr 2026 - 2:37

score 295 · Answer 14 · 2026-04-14 14:19:10

295

Views

Splitting field of $X^2-2$

Published on 14 Apr 2026 - 14:19

score 72 · Answer 15 · 2026-04-14 06:19:32

72

Views

A proof that two subfields of the same finite field equal if they have the same size

Published on 14 Apr 2026 - 6:19

List Question

If $f=\prod_{k=1}^m f_k$ in $L[X]$ show that there is an automorphism in $L$ such that $f_k^{\sigma }=f_j$

Degree and Galois group of $\mathbb{Q}(\sqrt[3]{2},\sqrt{-3})/\mathbb{Q}(\sqrt{-3})$.

All roots of $X^{p^r}-a$ are equal?

Factorization of $x^3-10x+4$ over $\mathbb Q(\sqrt 2, \sqrt[3] 2)$

Question about the proof of: $E/k$ is algebraic of characteristic zero. Every $f(x)\in k[x]$ has a root in $E$. Then $E$ is algebraically closed.

Are $\mathbb{C}(x)\otimes_\mathbb{R}\mathbb{C}(y)$ and $\mathbb{C}(x)\otimes_\mathbb{C}\mathbb{C}(y)$ integral domains or fields?

Does there exist a Cauchy-complete, non-Archimedean ordered field that is not isomorphic to a field extension of $\mathbb{R}$?

Generalizations of Algebraic Closures

necessary and sufficient conditions so that $\mathbb{Q}(\alpha)$ and $\mathbb{Q}(\beta)$ are isomorphic

Prove there is no field F satisfying R ⊊ F ⊊ C

If $a^n = a$ for all $a \in K$, what is $\operatorname{char} K$?

Suppose $B$ lies over $A$, s.t. $A,B$ integral domains. Does this tell us anything about which homomorphisms from $A$ to a field we can extend to $B$?

Natural irrationalities for infinite Galois extensions

Splitting field of $X^2-2$

A proof that two subfields of the same finite field equal if they have the same size

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