Question

Counting elements with prescribed trace and norm in finite field extension.

score 202 · Answer 1 · 2026-04-10 13:52:02

202

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Counting elements with prescribed trace and norm in finite field extension.

Published on 10 Apr 2026 - 13:52

score 394 · Answer 2 · 2026-04-14 08:04:08

394

Views

Isomorphism between tensor products (base extension)

Published on 14 Apr 2026 - 8:04

score 93 · Answer 3 · 2026-04-14 11:21:58

93

Views

Constructing a principal ideal of norm $2$ in $K = \mathbb{Q}(√(-23))$

Published on 14 Apr 2026 - 11:21

score 2.4k · Answer 4 · 2026-04-14 04:43:31

2.4k

Views

Can I prove that a splitting field is normal without using zorn lemma

Published on 14 Apr 2026 - 4:43

score 52 · Answer 5 · 2026-04-25 06:59:15

52

Views

The Order of an Especial Element in the Binary Finite Field

Published on 25 Apr 2026 - 6:59

score 40 · Answer 6 · 2026-04-16 17:10:56

40

Views

Degrees of extensions by $\alpha_1,\dots,\alpha_p$ of $\mathbb Q$ and $ L$ where $ \mathbb Q \leq L$

Published on 16 Apr 2026 - 17:10

score 900 · Answer 7 · 2026-04-14 15:38:17

900

Views

Galois groups of quartic over $\mathbb Q$ and $\mathbb Q(i)$

Published on 14 Apr 2026 - 15:38

score 762 · Answer 8 · 2026-04-16 13:22:00

762

Views

For two algebraically closed fields, one is isomorphic to a subfield of the other

Published on 16 Apr 2026 - 13:22

score 81 · Answer 9 · 2026-04-25 06:53:23

81

Views

Dimensions of Field Extensions

Published on 25 Apr 2026 - 6:53

score 37 · Answer 10 · 2026-04-11 07:08:52

37

Views

What is wrong in my reasoning on field extensions?

Published on 11 Apr 2026 - 7:08

score 194 · Answer 11 · 2026-03-26 06:31:47

194

Views

Elementary result: If $m>n$, then any $f_1,...,f_m$ (non-zero polynomials) in $K[X_1,...,X_n]$ are algebraically dependent over $K$

Published on 26 Mar 2026 - 6:31

score 557 · Answer 12 · 2026-04-16 18:59:27

557

Views

Find all field homomorphisms of $\mathbb{Q}(\sqrt[3]{2})$ and $\mathbb{Q}(\sqrt[3]{2}, \sqrt[3]{2} e^{\frac{2 \pi i}{3}})$

Published on 16 Apr 2026 - 18:59

score 7.3k · Answer 13 · 2026-04-17 04:27:47

7.3k

Views

Degree of $\sqrt{2}+\sqrt[3]{5}$ over $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(\sqrt[3]{5})$

Published on 17 Apr 2026 - 4:27

score 1.4k · Answer 14 · 2026-04-17 03:28:59

1.4k

Views

Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible

Published on 17 Apr 2026 - 3:28

score 1.7k · Answer 15 · 2026-04-13 20:30:41

1.7k

Views

Set of elements in $K$ that are purely inseparable over $F$ is a subfield

Published on 13 Apr 2026 - 20:30

List Question

Counting elements with prescribed trace and norm in finite field extension.

Isomorphism between tensor products (base extension)

Constructing a principal ideal of norm $2$ in $K = \mathbb{Q}(√(-23))$

Can I prove that a splitting field is normal without using zorn lemma

The Order of an Especial Element in the Binary Finite Field

Degrees of extensions by $\alpha_1,\dots,\alpha_p$ of $\mathbb Q$ and $ L$ where $ \mathbb Q \leq L$

Galois groups of quartic over $\mathbb Q$ and $\mathbb Q(i)$

For two algebraically closed fields, one is isomorphic to a subfield of the other

Dimensions of Field Extensions

What is wrong in my reasoning on field extensions?

Elementary result: If $m>n$, then any $f_1,...,f_m$ (non-zero polynomials) in $K[X_1,...,X_n]$ are algebraically dependent over $K$

Find all field homomorphisms of $\mathbb{Q}(\sqrt[3]{2})$ and $\mathbb{Q}(\sqrt[3]{2}, \sqrt[3]{2} e^{\frac{2 \pi i}{3}})$

Degree of $\sqrt{2}+\sqrt[3]{5}$ over $\mathbb{Q}(\sqrt{2})$ and $\mathbb{Q}(\sqrt[3]{5})$

Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible

Set of elements in $K$ that are purely inseparable over $F$ is a subfield

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