Question

Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same

score 5k · Answer 1 · 2026-04-15 21:12:17

5k

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Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same

Published on 15 Apr 2026 - 21:12

score 686 · Answer 2 · 2026-04-17 13:26:09

686

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Is there no field isomorphism between $k(x)$ and $k(x,y)$ for $k=\Bbb R$ or $\Bbb C$?

Published on 17 Apr 2026 - 13:26

score 215 · Answer 3 · 2026-04-16 10:57:21

215

Views

Prove that $S=\{f(\pi^5):f(x)\in \Bbb Q[x]\}$ is not a sub field of $\Bbb C$

Published on 16 Apr 2026 - 10:57

score 214 · Answer 4 · 2026-04-14 16:03:18

214

Views

7 roots of unity in finite field with characteristic two

Published on 14 Apr 2026 - 16:03

score 56 · Answer 5 · 2026-04-15 04:50:25

56

Views

Transitive subgroup of $\mathcal{S}_n$ implies normality for that subgroup?

Published on 15 Apr 2026 - 4:50

score 184 · Answer 6 · 2026-04-16 13:23:41

184

Views

Is there a way I can find out the degree of this extension without explicitly finding the minimal polynomial?

Published on 16 Apr 2026 - 13:23

score 161 · Answer 7 · 2026-04-09 21:39:39

161

Views

How do I show a particular polynomial has Galois group $Z_3$?

Published on 09 Apr 2026 - 21:39

score 967 · Answer 8 · 2026-04-14 21:23:05

967

Views

Show that any cyclic group with square free order is the Galois group over $\mathbb{Q}$ of some field extension

Published on 14 Apr 2026 - 21:23

score 71 · Answer 9 · 2026-04-17 10:13:14

71

Views

Constructing two non-isomorphic irreducible $\mathbb Q[x]$ modules with the underlying abelian group $\mathbb Q\times\mathbb Q$.

Published on 17 Apr 2026 - 10:13

score 304 · Answer 10 · 2026-04-11 07:35:06

304

Views

Finitely generated as a field vs. as an algebra?

Published on 11 Apr 2026 - 7:35

score 61 · Answer 11 · 2026-04-08 17:47:31

61

Views

Understanding of Definition of Field Homomorphism

Published on 08 Apr 2026 - 17:47

score 94 · Answer 12 · 2026-04-17 06:33:43

94

Views

Galois group of a field

Published on 17 Apr 2026 - 6:33

score 232 · Answer 13 · 2026-04-14 07:48:01

232

Views

Field not algebraic over an intersection but algebraic over each original field

Published on 14 Apr 2026 - 7:48

score 383 · Answer 14 · 2026-04-11 06:29:54

383

Views

Is the norm of a degree 2 extension surjective?

Published on 11 Apr 2026 - 6:29

score 558 · Answer 15 · 2026-04-15 07:31:42

558

Views

Will changing a field affect linear dependence/ linear independence of the given vector set

Published on 15 Apr 2026 - 7:31

List Question

Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same

Is there no field isomorphism between $k(x)$ and $k(x,y)$ for $k=\Bbb R$ or $\Bbb C$?

Prove that $S=\{f(\pi^5):f(x)\in \Bbb Q[x]\}$ is not a sub field of $\Bbb C$

7 roots of unity in finite field with characteristic two

Transitive subgroup of $\mathcal{S}_n$ implies normality for that subgroup?

Is there a way I can find out the degree of this extension without explicitly finding the minimal polynomial?

How do I show a particular polynomial has Galois group $Z_3$?

Show that any cyclic group with square free order is the Galois group over $\mathbb{Q}$ of some field extension

Constructing two non-isomorphic irreducible $\mathbb Q[x]$ modules with the underlying abelian group $\mathbb Q\times\mathbb Q$.

Finitely generated as a field vs. as an algebra?

Understanding of Definition of Field Homomorphism

Galois group of a field

Field not algebraic over an intersection but algebraic over each original field

Is the norm of a degree 2 extension surjective?

Will changing a field affect linear dependence/ linear independence of the given vector set

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