Question

If $E/F$ and $K/E$ are simple extensions, then $K/F$ is simple?

score 60 · Answer 1 · 2024-01-02 22:05:22

60

Views

If $E/F$ and $K/E$ are simple extensions, then $K/F$ is simple?

Published on 02 Jan 2024 - 22:05

score 40 · Answer 2 · 2024-01-03 17:34:01

40

Views

Degree of algebraically closed field extensions

Published on 03 Jan 2024 - 17:34

score 81 · Answer 3 · 2026-03-25 21:51:13

81

Views

Show that $A[T]/(P(T))$ is a local flat A-algebra where $(A,\mathfrak{m},k)$ is a local ring with $k[T]/(\tilde{P}(T))$ is a simple extension of $k$

Published on 25 Mar 2026 - 21:51

score 89 · Answer 4 · 2024-01-05 19:36:04

89

Views

$K[\alpha]=K(\alpha)$ (if and) only if $\alpha$ is algebraic?

Published on 05 Jan 2024 - 19:36

score 105 · Answer 5 · 2024-01-06 19:16:33

105

Views

Field homomorphism $\phi: F \to F$ with $F$ extension over $\mathbb{Q}$ is identity map

Published on 06 Jan 2024 - 19:16

score 3.3k · Answer 6 · 2024-01-09 19:27:18

3.3k

Views

Why can't we extend any field by simply adding a new symbol to it?

Published on 09 Jan 2024 - 19:27

score 69 · Answer 7 · 2024-01-10 18:58:58

69

Views

Help understanding proof of $\text{Tr}_{M/K}(\alpha) = \text{Tr}_{L/K}(\text{Tr}_{M/L}(\alpha)), \, \forall \alpha \in M$

Published on 10 Jan 2024 - 18:58

score 35 · Answer 8 · 2024-01-11 00:25:52

35

Views

Understanding proof of $\text{Tr}_{M/K}(\alpha) = \text{Tr}_{L/K}(\text{Tr}_{M/L}(\alpha)), \, \forall \alpha \in M$

Published on 11 Jan 2024 - 0:25

score 31 · Answer 9 · 2024-01-11 01:07:50

31

Views

For $K$ a field of characteristic $p$, $[K(X):K(X^p-X)]=p$.

Published on 11 Jan 2024 - 1:07

score 73 · Answer 10 · 2024-01-11 15:11:42

73

Views

Relations between field extensions of $\mathbb{Q}$

Published on 11 Jan 2024 - 15:11

score 177 · Answer 11 · 2024-01-12 10:34:51

177

Views

Proving $\sqrt[3]{5} \notin \mathbb{Q}(\sqrt[3]{2})$ with solvability of system in $\mathbb{Q}$

Published on 12 Jan 2024 - 10:34

score 51 · Answer 12 · 2026-03-29 12:39:20

51

Views

What is known of this problem similar to the inverse Galois problem? Galois groups of $\mathbb{Q}(X)/\mathbb{Q}(h(X))$ for $h \in \mathbb{Q}(X)$

Published on 29 Mar 2026 - 12:39

score 64 · Answer 13 · 2024-01-14 16:55:55

64

Views

Lagrange resolvent in field extensions

Published on 14 Jan 2024 - 16:55

score 67 · Answer 14 · 2024-01-15 14:19:55

67

Views

Questions of The Extension of Field

Published on 15 Jan 2024 - 14:19

score 126 · Answer 15 · 2024-01-15 22:37:14

126

Views

A commutative diagram for $F(\alpha) \cong F[x] / \langle p(x) \rangle$

Published on 15 Jan 2024 - 22:37

List Question

If $E/F$ and $K/E$ are simple extensions, then $K/F$ is simple?

Degree of algebraically closed field extensions

Show that $A[T]/(P(T))$ is a local flat A-algebra where $(A,\mathfrak{m},k)$ is a local ring with $k[T]/(\tilde{P}(T))$ is a simple extension of $k$

$K[\alpha]=K(\alpha)$ (if and) only if $\alpha$ is algebraic?

Field homomorphism $\phi: F \to F$ with $F$ extension over $\mathbb{Q}$ is identity map

Why can't we extend any field by simply adding a new symbol to it?

Help understanding proof of $\text{Tr}_{M/K}(\alpha) = \text{Tr}_{L/K}(\text{Tr}_{M/L}(\alpha)), \, \forall \alpha \in M$

Understanding proof of $\text{Tr}_{M/K}(\alpha) = \text{Tr}_{L/K}(\text{Tr}_{M/L}(\alpha)), \, \forall \alpha \in M$

For $K$ a field of characteristic $p$, $[K(X):K(X^p-X)]=p$.

Relations between field extensions of $\mathbb{Q}$

Proving $\sqrt[3]{5} \notin \mathbb{Q}(\sqrt[3]{2})$ with solvability of system in $\mathbb{Q}$

What is known of this problem similar to the inverse Galois problem? Galois groups of $\mathbb{Q}(X)/\mathbb{Q}(h(X))$ for $h \in \mathbb{Q}(X)$

Lagrange resolvent in field extensions

Questions of The Extension of Field

A commutative diagram for $F(\alpha) \cong F[x] / \langle p(x) \rangle$

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