Question

Extended of algebraically independent set

score 109 · Answer 1 · 2026-04-13 02:19:05

109

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Extended of algebraically independent set

Published on 13 Apr 2026 - 2:19

score 124 · Answer 2 · 2026-04-11 16:45:34

124

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How to check if an element $b$ belongs to $\Bbb Q(a)$

Published on 11 Apr 2026 - 16:45

score 83 · Answer 3 · 2026-04-17 07:29:11

83

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Add and multiplying disjoint algebraically independent sets are still disjoint algebraically independent sets

Published on 17 Apr 2026 - 7:29

score 178 · Answer 4 · 2026-04-15 19:33:42

178

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How to distinguish quadratic ramified extensions of $\mathbb Q_p$?

Published on 15 Apr 2026 - 19:33

score 287 · Answer 5 · 2026-04-14 07:25:46

287

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Maximal degree of irreducible polynomials

Published on 14 Apr 2026 - 7:25

score 38 · Answer 6 · 2026-04-14 05:39:59

38

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Let $(K,|\cdot|_K)$ be a complete valuation field. Prove that if $[L:K]<\infty$ then $R_L$ is the integral closure of $R_K$ in $L$.

Published on 14 Apr 2026 - 5:39

score 335 · Answer 7 · 2026-04-16 01:59:03

335

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How to prove that $p(x)$ is irreducible in $\mathbb{Q}(b)[x]$ if and only if $q(x)$ is irreducible in $\mathbb{Q}(a)[x]$

Published on 16 Apr 2026 - 1:59

score 287 · Answer 8 · 2026-04-11 10:41:55

287

Views

Every polynomial has a root in some extension field - why is irreducibility needed in construction?

Published on 11 Apr 2026 - 10:41

score 61 · Answer 9 · 2026-04-07 18:28:26

61

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field extension with degree of 2

Published on 07 Apr 2026 - 18:28

score 118 · Answer 10 · 2026-04-15 02:53:16

118

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Proving that a L-algebraic Set is also a K-algebraic set

Published on 15 Apr 2026 - 2:53

score 197 · Answer 11 · 2026-04-16 11:54:04

197

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Ambiguity regarding $\mathbb Q(\sqrt[4]{-2})$

Published on 16 Apr 2026 - 11:54

score 49 · Answer 12 · 2026-04-18 01:48:03

49

Views

Show that if $\zeta =e^{\frac{2\pi i}{n}}$, then $\mathbb{Q}(\zeta)=\{q_0+q_1 \zeta + \dots + q_{n-1}\zeta^{n-1}: q_i \in \mathbb{Q}\}$.

Published on 18 Apr 2026 - 1:48

score 80 · Answer 13 · 2026-04-16 06:28:11

80

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Question about quadratic field extension of $\mathbb{Q}$

Published on 16 Apr 2026 - 6:28

score 128 · Answer 14 · 2026-04-12 10:04:07

128

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Quadratic extensions of function fields

Published on 12 Apr 2026 - 10:04

score 111 · Answer 15 · 2026-04-14 03:02:47

111

Views

Dimension $\mathbb {R}(\mathbb {C})$ versus dimension $\mathbb {C}(\mathbb {R})$

Published on 14 Apr 2026 - 3:02

List Question

Extended of algebraically independent set

How to check if an element $b$ belongs to $\Bbb Q(a)$

Add and multiplying disjoint algebraically independent sets are still disjoint algebraically independent sets

How to distinguish quadratic ramified extensions of $\mathbb Q_p$?

Maximal degree of irreducible polynomials

Let $(K,|\cdot|_K)$ be a complete valuation field. Prove that if $[L:K]<\infty$ then $R_L$ is the integral closure of $R_K$ in $L$.

How to prove that $p(x)$ is irreducible in $\mathbb{Q}(b)[x]$ if and only if $q(x)$ is irreducible in $\mathbb{Q}(a)[x]$

Every polynomial has a root in some extension field - why is irreducibility needed in construction?

field extension with degree of 2

Proving that a L-algebraic Set is also a K-algebraic set

Ambiguity regarding $\mathbb Q(\sqrt[4]{-2})$

Show that if $\zeta =e^{\frac{2\pi i}{n}}$, then $\mathbb{Q}(\zeta)=\{q_0+q_1 \zeta + \dots + q_{n-1}\zeta^{n-1}: q_i \in \mathbb{Q}\}$.

Question about quadratic field extension of $\mathbb{Q}$

Quadratic extensions of function fields

Dimension $\mathbb {R}(\mathbb {C})$ versus dimension $\mathbb {C}(\mathbb {R})$

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