Question

Is the definition of a transcendental field extension necessarily impredicative?

score 59 · Answer 1 · 2026-03-25 13:56:53

59

Views

Is the definition of a transcendental field extension necessarily impredicative?

Published on 25 Mar 2026 - 13:56

score 277 · Answer 2 · 2026-04-02 05:25:53

277

Views

The only non-trivial Homomorphic images of a field $F$ is $F$-------Is the statement true?

Published on 02 Apr 2026 - 5:25

score 975 · Answer 3 · 2026-04-02 05:27:43

975

Views

Showing $[\mathbb{Q}(2^{1/3},2^{1/2}):\mathbb{Q}(2^{1/2})]=3$

Published on 02 Apr 2026 - 5:27

score 441 · Answer 4 · 2026-04-02 05:22:39

441

Views

Finding the splitting field $K$ of $x^4+x^2+1$ over $\mathbb{Q}$ and $[K:\mathbb{Q}]$

Published on 02 Apr 2026 - 5:22

score 1.7k · Answer 5 · 2026-03-29 20:02:20

1.7k

Views

Showing that all elements of a Field Extension are transcendental

Published on 29 Mar 2026 - 20:02

score 194 · Answer 6 · 2018-11-01 12:38:49

194

Views

Ring of integers of the maximal totally real subfield of CM field.

Published on 01 Nov 2018 - 12:38

score 61 · Answer 7 · 2026-03-27 12:03:10

61

Views

if $L/F$ a field extension, if b is algebraic over $F(a)$ and $b$ not algebraic over $F$, then $a$ is algebraic over $F(b)$. Example?

Published on 27 Mar 2026 - 12:03

score 482 · Answer 8 · 2026-03-30 00:22:47

482

Views

What is the number of irreducible factors of $x^{255}-1$ over $\mathbb{Q}$ and $\mathbb{F}_2$?

Published on 30 Mar 2026 - 0:22

score 203 · Answer 9 · 2026-03-27 04:35:14

203

Views

Finite field where each subgroup of the multiplicative group of nonzero elements of the field, together with $0$, forms a field.

Published on 27 Mar 2026 - 4:35

score 513 · Answer 10 · 2026-03-27 14:53:49

513

Views

How can I prove that any field of order $p^n$ has a unique subring of order $p^m$ where $m$ divides $n$.

Published on 27 Mar 2026 - 14:53

score 58 · Answer 11 · 2026-03-27 11:50:00

58

Views

$S_m(F)=\{a\in F:a^{p^m}=a\}$. $S_m (F)$ is a subfield of the field $F$.

Published on 27 Mar 2026 - 11:50

score 182 · Answer 12 · 2026-03-30 00:19:51

182

Views

Counterexample for size of field automorphism group

Published on 30 Mar 2026 - 0:19

score 339 · Answer 13 · 2026-03-29 19:57:48

339

Views

An alternate proof for $[K:Q] = 2$ then $K = Q(\sqrt{d}), d$ square free

Published on 29 Mar 2026 - 19:57

score 128 · Answer 14 · 2018-11-05 14:09:36

128

Views

A property of fields

Published on 05 Nov 2018 - 14:09

score 736 · Answer 15 · 2026-03-26 02:57:47

736

Views

Let $F$ be a field, when is the quotient ring $F[x]/(x^2+1)F[x]$ an integral domain?

Published on 26 Mar 2026 - 2:57

List Question

Is the definition of a transcendental field extension necessarily impredicative?

The only non-trivial Homomorphic images of a field $F$ is $F$-------Is the statement true?

Showing $[\mathbb{Q}(2^{1/3},2^{1/2}):\mathbb{Q}(2^{1/2})]=3$

Finding the splitting field $K$ of $x^4+x^2+1$ over $\mathbb{Q}$ and $[K:\mathbb{Q}]$

Showing that all elements of a Field Extension are transcendental

Ring of integers of the maximal totally real subfield of CM field.

if $L/F$ a field extension, if b is algebraic over $F(a)$ and $b$ not algebraic over $F$, then $a$ is algebraic over $F(b)$. Example?

What is the number of irreducible factors of $x^{255}-1$ over $\mathbb{Q}$ and $\mathbb{F}_2$?

Finite field where each subgroup of the multiplicative group of nonzero elements of the field, together with $0$, forms a field.

How can I prove that any field of order $p^n$ has a unique subring of order $p^m$ where $m$ divides $n$.

$S_m(F)=\{a\in F:a^{p^m}=a\}$. $S_m (F)$ is a subfield of the field $F$.

Counterexample for size of field automorphism group

An alternate proof for $[K:Q] = 2$ then $K = Q(\sqrt{d}), d$ square free

A property of fields

Let $F$ be a field, when is the quotient ring $F[x]/(x^2+1)F[x]$ an integral domain?

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