Question

Let $F$ be an infinite field. Then is it true that there does not exist any surjection from $F$ onto $F[x]$?

score 104 · Answer 1 · 2026-04-15 03:31:49

104

Views

Let $F$ be an infinite field. Then is it true that there does not exist any surjection from $F$ onto $F[x]$?

Published on 15 Apr 2026 - 3:31

score 78 · Answer 2 · 2026-04-14 18:06:06

78

Views

Sum, product and real part of numbers $z$ such that $\Bbb Q(z)/\Bbb Q$ is Galois.

Published on 14 Apr 2026 - 18:06

score 714 · Answer 3 · 2026-04-15 13:51:54

714

Views

Isomorphism between $\Bbb R$ and $\Bbb R(X)$?

Published on 15 Apr 2026 - 13:51

score 689 · Answer 4 · 2026-04-11 15:13:46

689

Views

How to prove $x^{2k}+1$ is irreducible over the rational numbers

Published on 11 Apr 2026 - 15:13

score 481 · Answer 5 · 2026-04-12 22:25:29

481

Views

Factoring a prime over a splitting field and factoring a polynomial over of a finite field

Published on 12 Apr 2026 - 22:25

score 285 · Answer 6 · 2026-04-16 14:18:53

285

Views

If $\Bbb Q[x,y]$ is a field, are $x$ and $y$ algebraic over $\Bbb Q$?

Published on 16 Apr 2026 - 14:18

score 315 · Answer 7 · 2026-04-16 12:26:47

315

Views

Galois group of $\Bbb Q(\{\sqrt[2^n]{2}, \zeta_{2^n} \;:\; n \geq 1 \})$ over $\Bbb Q$

Published on 16 Apr 2026 - 12:26

score 290 · Answer 8 · 2026-04-11 23:45:39

290

Views

The product map and the inverse map are continuous with respect to the Krull topology

Published on 11 Apr 2026 - 23:45

score 302 · Answer 9 · 2026-03-25 13:34:19

302

Views

Determine all $P(X)\in K[X]$ such that $P\big(X^2+1\big)=\big(P(X)\big)^2+1$, for fields $K$ of any characteristic.

Published on 25 Mar 2026 - 13:34

score 453 · Answer 10 · 2026-04-12 06:59:38

453

Views

Is $K(X)$ never algebraically closed?

Published on 12 Apr 2026 - 6:59

score 2.9k · Answer 11 · 2026-04-16 11:58:54

2.9k

Views

Find the Galois group of $x^3-2$ over the field $\mathbb F_5$

Published on 16 Apr 2026 - 11:58

score 773 · Answer 12 · 2026-04-15 03:14:11

773

Views

$\sqrt{p_1}$ is not in $Q[\sqrt{p_2},...,\sqrt{p_n}]$

Published on 15 Apr 2026 - 3:14

score 733 · Answer 13 · 2026-04-13 12:43:04

733

Views

Non-isomorphic quadratic fields

Published on 13 Apr 2026 - 12:43

score 132 · Answer 14 · 2026-04-14 03:13:17

132

Views

When are extensions $k(x)/k(s)$ for points in the fiber of a closed point algebraic?

Published on 14 Apr 2026 - 3:13

score 2.5k · Answer 15 · 2026-04-14 04:32:41

2.5k

Views

The field extension $\mathbb{C}/\mathbb{Q}$ is infinite

Published on 14 Apr 2026 - 4:32

List Question

Let $F$ be an infinite field. Then is it true that there does not exist any surjection from $F$ onto $F[x]$?

Sum, product and real part of numbers $z$ such that $\Bbb Q(z)/\Bbb Q$ is Galois.

Isomorphism between $\Bbb R$ and $\Bbb R(X)$?

How to prove $x^{2k}+1$ is irreducible over the rational numbers

Factoring a prime over a splitting field and factoring a polynomial over of a finite field

If $\Bbb Q[x,y]$ is a field, are $x$ and $y$ algebraic over $\Bbb Q$?

Galois group of $\Bbb Q(\{\sqrt[2^n]{2}, \zeta_{2^n} \;:\; n \geq 1 \})$ over $\Bbb Q$

The product map and the inverse map are continuous with respect to the Krull topology

Determine all $P(X)\in K[X]$ such that $P\big(X^2+1\big)=\big(P(X)\big)^2+1$, for fields $K$ of any characteristic.

Is $K(X)$ never algebraically closed?

Find the Galois group of $x^3-2$ over the field $\mathbb F_5$

$\sqrt{p_1}$ is not in $Q[\sqrt{p_2},...,\sqrt{p_n}]$

Non-isomorphic quadratic fields

When are extensions $k(x)/k(s)$ for points in the fiber of a closed point algebraic?

The field extension $\mathbb{C}/\mathbb{Q}$ is infinite

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