Question

tensor product of field and linearly independent

score 114 · Answer 1 · 2026-04-13 04:57:11

114

Views

tensor product of field and linearly independent

Published on 13 Apr 2026 - 4:57

score 288 · Answer 2 · 2026-04-16 07:24:30

288

Views

Field must be perfect or characteristic p

Published on 16 Apr 2026 - 7:24

score 63 · Answer 3 · 2026-04-16 05:12:35

63

Views

Number of invertible elements in a quadratic extension of a finite ring

Published on 16 Apr 2026 - 5:12

score 355 · Answer 4 · 2026-04-10 23:34:38

355

Views

Compositum of normal extensions

Published on 10 Apr 2026 - 23:34

score 569 · Answer 5 · 2026-04-15 16:03:26

569

Views

Conjugate subgroups of Galois Group iff Isomorphic Extensions

Published on 15 Apr 2026 - 16:03

score 238 · Answer 6 · 2026-04-15 06:15:10

238

Views

field isomorphism extension theorem and galois transitive action

Published on 15 Apr 2026 - 6:15

score 111 · Answer 7 · 2026-04-11 10:31:55

111

Views

Proof of Nilpotency of Matrix All Whose Powers Have Vanishing Trace Without Using Eigenvalues

Published on 11 Apr 2026 - 10:31

score 112 · Answer 8 · 2026-04-11 23:15:17

112

Views

Why does the definition of a fixed field specify a subgroup of the Galois group, not just a subset?

Published on 11 Apr 2026 - 23:15

score 136 · Answer 9 · 2026-04-14 08:47:44

136

Views

If $S\to C$ is surjective and $S$ is a rational surface, then $C\simeq \Bbb{P}^1$.

Published on 14 Apr 2026 - 8:47

score 208 · Answer 10 · 2026-04-14 05:33:04

208

Views

Finite extension $\Rightarrow$ a finite number of algebraic elements proof

Published on 14 Apr 2026 - 5:33

score 66 · Answer 11 · 2026-04-16 21:09:26

66

Views

Fields $k$ such that if a degree $n$ polynomial $f\in k[x]$ has $n$ distinct roots in $k$, then its derivative $f'$ has $n-1$ distinct roots in $k$.

Published on 16 Apr 2026 - 21:09

score 25 · Answer 12 · 2026-04-14 08:58:45

25

Views

Irreducible polynomial $x^n - P(y)$ in field extension when $P(y)$ is not constant and not has repeated factors

Published on 14 Apr 2026 - 8:58

score 55 · Answer 13 · 2026-04-30 11:04:15

55

Views

Extended automorphisms

Published on 30 Apr 2026 - 11:04

score 63 · Answer 14 · 2026-04-11 04:02:49

63

Views

Ring automorphism extending to subrings

Published on 11 Apr 2026 - 4:02

score 61 · Answer 15 · 2026-04-12 22:37:19

61

Views

What does it mean for two field extensions over $\mathbb{Q}$ to be "$\mathbb{Q}$-isomorphic?"

Published on 12 Apr 2026 - 22:37

List Question

tensor product of field and linearly independent

Field must be perfect or characteristic p

Number of invertible elements in a quadratic extension of a finite ring

Compositum of normal extensions

Conjugate subgroups of Galois Group iff Isomorphic Extensions

field isomorphism extension theorem and galois transitive action

Proof of Nilpotency of Matrix All Whose Powers Have Vanishing Trace Without Using Eigenvalues

Why does the definition of a fixed field specify a subgroup of the Galois group, not just a subset?

If $S\to C$ is surjective and $S$ is a rational surface, then $C\simeq \Bbb{P}^1$.

Finite extension $\Rightarrow$ a finite number of algebraic elements proof

Fields $k$ such that if a degree $n$ polynomial $f\in k[x]$ has $n$ distinct roots in $k$, then its derivative $f'$ has $n-1$ distinct roots in $k$.

Irreducible polynomial $x^n - P(y)$ in field extension when $P(y)$ is not constant and not has repeated factors

Extended automorphisms

Ring automorphism extending to subrings

What does it mean for two field extensions over $\mathbb{Q}$ to be "$\mathbb{Q}$-isomorphic?"

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