Question

Write $x^3 + 2x+1$ as a product of linear polynomials over some extension field of $\mathbb{Z}_3$

score 2k · Answer 1 · 2026-04-15 11:19:09

2k

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Write $x^3 + 2x+1$ as a product of linear polynomials over some extension field of $\mathbb{Z}_3$

Published on 15 Apr 2026 - 11:19

score 93 · Answer 2 · 2026-04-18 04:37:11

93

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Why is $L=\mathbb{Q}(\sqrt[1]{2})\cup\mathbb{Q}(\sqrt[2]{2})\cup\mathbb{Q}(\sqrt[3]{2})\cup\cdots$ a field?

Published on 18 Apr 2026 - 4:37

score 79 · Answer 3 · 2026-04-13 09:36:20

79

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Are these fields splitting fields?

Published on 13 Apr 2026 - 9:36

score 185 · Answer 4 · 2026-04-14 13:06:54

185

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Show that $\mathbb{K}$ is a field

Published on 14 Apr 2026 - 13:06

score 75 · Answer 5 · 2026-04-16 06:43:00

75

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How do you find the elements of $\mathbb{F} _5 [x] / (x^2 + 2)$?

Published on 16 Apr 2026 - 6:43

score 423 · Answer 6 · 2026-04-15 20:40:44

423

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Reducing $x^3-\sqrt{2}$ over $\mathbb{Q}(\sqrt{2})[x]$

Published on 15 Apr 2026 - 20:40

score 72 · Answer 7 · 2026-04-16 08:53:26

72

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Let $E/K$ be an algebraic extension. Is $E/(E\cap K^{1/p^\infty})$ necessarily separable?

Published on 16 Apr 2026 - 8:53

score 1.3k · Answer 8 · 2026-04-13 00:38:44

1.3k

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Quadratic extension of field of characteristic 2 can/cannot be obtained by adjoining a single square root

Published on 13 Apr 2026 - 0:38

score 752 · Answer 9 · 2026-04-12 01:53:16

752

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Are those properties sufficient for defining a field?

Published on 12 Apr 2026 - 1:53

score 1.1k · Answer 10 · 2026-04-13 07:04:29

1.1k

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Subfield of a finitely generated field extension is still finitely generated

Published on 13 Apr 2026 - 7:04

score 278 · Answer 11 · 2026-04-12 13:53:38

278

Views

Non-linear cyclic order of a field

Published on 12 Apr 2026 - 13:53

score 261 · Answer 12 · 2026-05-11 09:47:58

261

Views

Prove that: Any field containing $Z[i]$ as a subring contains $Q[i]$ as a subfield.

Published on 11 May 2026 - 9:47

score 51 · Answer 13 · 2026-04-10 18:24:54

51

Views

Is this an example for $[E:\Bbb R]$=4?

Published on 10 Apr 2026 - 18:24

score 54 · Answer 14 · 2026-04-11 17:20:23

54

Views

Determine the minimal polynomial

Published on 11 Apr 2026 - 17:20

score 62 · Answer 15 · 2026-04-16 22:54:10

Show that $\mathbb{Q}(\sqrt{n},\sqrt{-n})\subseteq\mathbb{Q}(\sqrt{n}+\sqrt{-n})$ by evaluating $\alpha^3+2n\alpha$ and $\alpha^3-2n\alpha$

List Question

Write $x^3 + 2x+1$ as a product of linear polynomials over some extension field of $\mathbb{Z}_3$

Why is $L=\mathbb{Q}(\sqrt[1]{2})\cup\mathbb{Q}(\sqrt[2]{2})\cup\mathbb{Q}(\sqrt[3]{2})\cup\cdots$ a field?

Are these fields splitting fields?

Show that $\mathbb{K}$ is a field

How do you find the elements of $\mathbb{F} _5 [x] / (x^2 + 2)$?

Reducing $x^3-\sqrt{2}$ over $\mathbb{Q}(\sqrt{2})[x]$

Let $E/K$ be an algebraic extension. Is $E/(E\cap K^{1/p^\infty})$ necessarily separable?

Quadratic extension of field of characteristic 2 can/cannot be obtained by adjoining a single square root

Are those properties sufficient for defining a field?

Subfield of a finitely generated field extension is still finitely generated

Non-linear cyclic order of a field

Prove that: Any field containing $Z[i]$ as a subring contains $Q[i]$ as a subfield.

Is this an example for $[E:\Bbb R]$=4?

Determine the minimal polynomial

Show that $\mathbb{Q}(\sqrt{n},\sqrt{-n})\subseteq\mathbb{Q}(\sqrt{n}+\sqrt{-n})$ by evaluating $\alpha^3+2n\alpha$ and $\alpha^3-2n\alpha$

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