Question

Prove that $X_1+2X_2+\cdots+nX_n$ is a primitive element in a field extension of rational functions

score 50 · Answer 1 · 2019-09-02 15:23:45

50

Views

Prove that $X_1+2X_2+\cdots+nX_n$ is a primitive element in a field extension of rational functions

Published on 02 Sep 2019 - 15:23

score 54 · Answer 2 · 2026-04-01 07:57:22

54

Views

Algebraic extension

Published on 01 Apr 2026 - 7:57

score 155 · Answer 3 · 2026-03-29 07:38:44

155

Views

Showing that $\mathbb{Q}(\sqrt{2}) \subseteq \mathbb{Q}(\sqrt{2}+\sqrt[3]{2})$

Published on 29 Mar 2026 - 7:38

score 99 · Answer 4 · 2019-09-03 11:25:24

99

Views

When does the extension of scalars to $\mathbf Q$ give the field of fractions?

Published on 03 Sep 2019 - 11:25

score 59 · Answer 5 · 2026-03-29 19:16:38

59

Views

The set of subfields is totally ordered

Published on 29 Mar 2026 - 19:16

score 327 · Answer 6 · 2026-04-02 09:15:40

327

Views

Is $\mathbb{Q}(\sin\frac{2\pi}{n})$ Galois over $\mathbb{Q}$?

Published on 02 Apr 2026 - 9:15

score 207 · Answer 7 · 2026-03-24 22:08:44

207

Views

What is the genus of an unramified extension of a function field?

Published on 24 Mar 2026 - 22:08

score 142 · Answer 8 · 2026-03-26 01:34:22

142

Views

Find an example about splitting field

Published on 26 Mar 2026 - 1:34

score 245 · Answer 9 · 2026-04-07 01:52:46

245

Views

Without using Dirichlet's theorem, show that there are infinitely primes congruent to $a$ mod n if $a^2\equiv 1\,(\!\bmod\; n)$

Published on 07 Apr 2026 - 1:52

score 67 · Answer 10 · 2026-04-01 07:55:33

67

Views

The dimension of $F(X)$ over field $F(P(X))$ is .......

Published on 01 Apr 2026 - 7:55

score 78 · Answer 11 · 2026-03-26 17:53:45

78

Views

If $-1$ is a sum of squares, then any element is a sum of squares

Published on 26 Mar 2026 - 17:53

score 59 · Answer 12 · 2026-03-29 08:44:38

59

Views

Is there a difference in fields notated as $k$ and $\mathbb{F}$ or is one just more modern

Published on 29 Mar 2026 - 8:44

score 501 · Answer 13 · 2026-03-28 03:52:52

501

Views

To prove that $\mathbb{Q}$ is the smallest subfield of $\mathbb{C}$

Published on 28 Mar 2026 - 3:52

score 326 · Answer 14 · 2026-03-26 03:00:53

326

Views

Are the fields $\mathbb{Q}$ and $\mathbb{Q[\sqrt2]}$ isomorphic?

Published on 26 Mar 2026 - 3:00

score 49 · Answer 15 · 2026-03-29 07:38:36

49

Views

Generalising a problem when two fields $F \ncong K$

Published on 29 Mar 2026 - 7:38

List Question

Prove that $X_1+2X_2+\cdots+nX_n$ is a primitive element in a field extension of rational functions

Algebraic extension

Showing that $\mathbb{Q}(\sqrt{2}) \subseteq \mathbb{Q}(\sqrt{2}+\sqrt[3]{2})$

When does the extension of scalars to $\mathbf Q$ give the field of fractions?

The set of subfields is totally ordered

Is $\mathbb{Q}(\sin\frac{2\pi}{n})$ Galois over $\mathbb{Q}$?

What is the genus of an unramified extension of a function field?

Find an example about splitting field

Without using Dirichlet's theorem, show that there are infinitely primes congruent to $a$ mod n if $a^2\equiv 1\,(\!\bmod\; n)$

The dimension of $F(X)$ over field $F(P(X))$ is .......

If $-1$ is a sum of squares, then any element is a sum of squares

Is there a difference in fields notated as $k$ and $\mathbb{F}$ or is one just more modern

To prove that $\mathbb{Q}$ is the smallest subfield of $\mathbb{C}$

Are the fields $\mathbb{Q}$ and $\mathbb{Q[\sqrt2]}$ isomorphic?

Generalising a problem when two fields $F \ncong K$

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