Question

Does there exist $\alpha \in \mathbb{R}$ and a field $F \subset \mathbb{R} $ such that $F(\alpha)=\mathbb{R}$?

score 498 · Answer 1 · 2026-03-27 23:53:22

498

Views

Does there exist $\alpha \in \mathbb{R}$ and a field $F \subset \mathbb{R} $ such that $F(\alpha)=\mathbb{R}$?

Published on 27 Mar 2026 - 23:53

score 82 · Answer 2 · 2026-04-13 17:41:08

82

Views

Constructing finite fields as quotients of a domain by its ideals

Published on 13 Apr 2026 - 17:41

score 209 · Answer 3 · 2026-03-26 12:34:38

209

Views

Without excluded middle: simple example of field with nilpotents?

Published on 26 Mar 2026 - 12:34

score 742 · Answer 4 · 2026-04-17 02:53:03

742

Views

Find all embedding field-homomorphisms $\sigma:\mathbb{Q}(5^{1/3})\to \mathbb{C}$

Published on 17 Apr 2026 - 2:53

score 92 · Answer 5 · 2026-04-09 21:17:46

92

Views

Explicit expression minimal polynomial which is equal to characteristic.

Published on 09 Apr 2026 - 21:17

score 72 · Answer 6 · 2026-04-16 10:37:04

72

Views

If $\alpha$ is algebraic over a Field, find a nonzero polynomial such that $q(\alpha^2) = 0$

Published on 16 Apr 2026 - 10:37

score 5.3k · Answer 7 · 2026-04-16 14:00:39

5.3k

Views

If derivative of an irreducible polynomial is non zero then the polynomial is separable

Published on 16 Apr 2026 - 14:00

score 330 · Answer 8 · 2026-04-14 00:42:34

330

Views

Galois group of $f(x^2)$

Published on 14 Apr 2026 - 0:42

score 67 · Answer 9 · 2026-04-16 20:48:17

67

Views

Prove or disprove: $\Bbb Q (\sqrt{3})$ is isomorphic to $\Bbb Q (-\sqrt{3})$.

Published on 16 Apr 2026 - 20:48

score 192 · Answer 10 · 2026-04-16 08:07:31

192

Views

Show that if $\gcd(q,q')\neq1$, then fields are isomorphic to sub-fields of some finite field

Published on 16 Apr 2026 - 8:07

score 299 · Answer 11 · 2026-04-17 03:45:24

299

Views

Dropping the condition in Hilbert's Nullstellensatz

Published on 17 Apr 2026 - 3:45

score 120 · Answer 12 · 2026-04-15 11:43:03

120

Views

Isomorphism in a field

Published on 15 Apr 2026 - 11:43

score 66 · Answer 13 · 2026-04-16 14:23:57

66

Views

If $(\mathbb{R}^2,+,\cdot)$ is a field, then there exists $u\in\mathbb{R}^2$ such that $u^2=-e$.

Published on 16 Apr 2026 - 14:23

score 43 · Answer 14 · 2026-04-13 03:01:47

43

Views

Splitting fields of polynomials

Published on 13 Apr 2026 - 3:01

score 666 · Answer 15 · 2026-04-16 08:10:24

666

Views

Non trivial automorphism of $\mathbb{Q}(\pi)$

Published on 16 Apr 2026 - 8:10

List Question

Does there exist $\alpha \in \mathbb{R}$ and a field $F \subset \mathbb{R} $ such that $F(\alpha)=\mathbb{R}$?

Constructing finite fields as quotients of a domain by its ideals

Without excluded middle: simple example of field with nilpotents?

Find all embedding field-homomorphisms $\sigma:\mathbb{Q}(5^{1/3})\to \mathbb{C}$

Explicit expression minimal polynomial which is equal to characteristic.

If $\alpha$ is algebraic over a Field, find a nonzero polynomial such that $q(\alpha^2) = 0$

If derivative of an irreducible polynomial is non zero then the polynomial is separable

Galois group of $f(x^2)$

Prove or disprove: $\Bbb Q (\sqrt{3})$ is isomorphic to $\Bbb Q (-\sqrt{3})$.

Show that if $\gcd(q,q')\neq1$, then fields are isomorphic to sub-fields of some finite field

Dropping the condition in Hilbert's Nullstellensatz

Isomorphism in a field

If $(\mathbb{R}^2,+,\cdot)$ is a field, then there exists $u\in\mathbb{R}^2$ such that $u^2=-e$.

Splitting fields of polynomials

Non trivial automorphism of $\mathbb{Q}(\pi)$

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