Question

If $a$ belongs to an extension field of $F$ and $f(a)$ is algebraic over $F$, then $a$ is algebraic over $F$.

score 130 · Answer 1 · 2026-04-16 09:48:51

130

Views

If $a$ belongs to an extension field of $F$ and $f(a)$ is algebraic over $F$, then $a$ is algebraic over $F$.

Published on 16 Apr 2026 - 9:48

score 465 · Answer 2 · 2026-04-15 08:11:25

465

Views

Any generalization of the complex conjugates in the theory of fields?

Published on 15 Apr 2026 - 8:11

score 30 · Answer 3 · 2026-04-29 01:01:19

30

Views

Find concise necessary and sufficient conditions on $a_0,a_1,....a_n$ for $\alpha$ to be a unit.

Published on 29 Apr 2026 - 1:01

score 40 · Answer 4 · 2026-04-15 22:08:26

40

Views

How many field homomorphisms are from $\mathbb{Q}[2^{1/3},2^{1/5}]$ to $\mathbb{C}$.

Published on 15 Apr 2026 - 22:08

score 41 · Answer 5 · 2026-04-10 01:13:50

41

Views

Confused About Irreducibility - Fraleigh

Published on 10 Apr 2026 - 1:13

score 77 · Answer 6 · 2026-03-29 18:37:21

77

Views

If $G$ is a finite group of automorphisms of $L/k$, then $\hom_k(L^G,k_s)=\hom_k(L,k_s)/G$.

Published on 29 Mar 2026 - 18:37

score 90 · Answer 7 · 2026-04-14 22:20:25

90

Views

Algebra qual problem: Algebraic extension of a real field

Published on 14 Apr 2026 - 22:20

score 29 · Answer 8 · 2026-04-12 22:59:49

29

Views

How $N(2\zeta^{2n})=2^{p-1}$?

Published on 12 Apr 2026 - 22:59

score 320 · Answer 9 · 2026-04-12 03:24:13

320

Views

Why every field is a local ring, but the ring of integers $\mathbb{Z}$ not?

Published on 12 Apr 2026 - 3:24

score 45 · Answer 10 · 2026-04-14 23:05:37

45

Views

Fields non-trivially seen to be isomorphic to the real numbers by the uniqueness of a complete ordered field

Published on 14 Apr 2026 - 23:05

score 141 · Answer 11 · 2026-03-29 02:46:09

141

Views

Non Abelian Normal Field Extension with Abelian Subextensions

Published on 29 Mar 2026 - 2:46

score 3.5k · Answer 12 · 2026-04-30 01:08:27

3.5k

Views

Why is the category of fields seemingly so poorly behaved?

Published on 30 Apr 2026 - 1:08

score 73 · Answer 13 · 2026-04-15 05:36:21

73

Views

Determinate the minimal polynomial of $\sqrt{a}$ where a is an algebraic complex number over $\mathbb{Q}$

Published on 15 Apr 2026 - 5:36

score 43 · Answer 14 · 2026-04-17 07:24:47

43

Views

Is it true that in general $\operatorname{Gal}(K:\mathbb{Q}_p)\cong\operatorname{Gal}(k:\mathbb{F}_{p^f})$?

Published on 17 Apr 2026 - 7:24

score 704 · Answer 15 · 2026-04-14 14:07:02

704

Views

Why isn't the zero ring the field with one element?

Published on 14 Apr 2026 - 14:07

List Question

If $a$ belongs to an extension field of $F$ and $f(a)$ is algebraic over $F$, then $a$ is algebraic over $F$.

Any generalization of the complex conjugates in the theory of fields?

Find concise necessary and sufficient conditions on $a_0,a_1,....a_n$ for $\alpha$ to be a unit.

How many field homomorphisms are from $\mathbb{Q}[2^{1/3},2^{1/5}]$ to $\mathbb{C}$.

Confused About Irreducibility - Fraleigh

If $G$ is a finite group of automorphisms of $L/k$, then $\hom_k(L^G,k_s)=\hom_k(L,k_s)/G$.

Algebra qual problem: Algebraic extension of a real field

How $N(2\zeta^{2n})=2^{p-1}$?

Why every field is a local ring, but the ring of integers $\mathbb{Z}$ not?

Fields non-trivially seen to be isomorphic to the real numbers by the uniqueness of a complete ordered field

Non Abelian Normal Field Extension with Abelian Subextensions

Why is the category of fields seemingly so poorly behaved?

Determinate the minimal polynomial of $\sqrt{a}$ where a is an algebraic complex number over $\mathbb{Q}$

Is it true that in general $\operatorname{Gal}(K:\mathbb{Q}_p)\cong\operatorname{Gal}(k:\mathbb{F}_{p^f})$?

Why isn't the zero ring the field with one element?

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