List questions from extension-field

147

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If two elements generate the same extension, is there a relationship between their minimal polynomials?

Published on 13 Apr 2026 - 2:13

190

Views

$F(a,b)$ separable if $F(a)$ and $F(b)$ are separable

Published on 16 Apr 2026 - 12:57

264

Views

Extensions with the same degree are $K-$isomorphic?

Published on 10 Apr 2026 - 8:25

47

Views

Inverse image of a "rational map" is "rational"

Published on 15 Apr 2026 - 20:26

59

Views

Factorize $f(X)=X^4+1$ on $L$.

Published on 14 Apr 2026 - 12:06

48

Views

Issue in the proof showing that the splitting fields are normal.

Published on 14 Apr 2026 - 9:38

73

Views

Is $G(\mathbb{Q}(\sqrt[3]{2}), i\sqrt{3})/\mathbb{Q}(i\sqrt{3}))\simeq \left \langle \mathbb{Z_3}, + \right \rangle$?

Published on 15 Apr 2026 - 18:08

241

Views

Adjoining element in a finite field $\mathbb F_{p^n}$ to $\mathbb F_p$ to get $\mathbb F_{p^6}$

Published on 17 Apr 2026 - 4:16

76

Views

Homomorphism between the Field F and the Quotient Ring of Polynomial Ring

Published on 15 Apr 2026 - 0:06

142

Views

Field automorphisms send roots into roots

Published on 14 Apr 2026 - 10:49

217

Views

A solvable galois group implies radical extension

Published on 13 Apr 2026 - 5:53

41

Views

Understanding field automorphisms

Published on 09 Apr 2026 - 0:32

82

Views

Does it matter whether we consider field extensions as true supersets of a field?

Published on 11 Apr 2026 - 6:15

260

Views

Decomposition of Field extensions and Transcendence basis

Published on 13 Apr 2026 - 18:44

253

Views

Transcendence basis as subset of generators

Published on 12 Apr 2026 - 4:24

List Question

If two elements generate the same extension, is there a relationship between their minimal polynomials?

$F(a,b)$ separable if $F(a)$ and $F(b)$ are separable

Extensions with the same degree are $K-$isomorphic?

Inverse image of a "rational map" is "rational"

Factorize $f(X)=X^4+1$ on $L$.

Issue in the proof showing that the splitting fields are normal.

Is $G(\mathbb{Q}(\sqrt[3]{2}), i\sqrt{3})/\mathbb{Q}(i\sqrt{3}))\simeq \left \langle \mathbb{Z_3}, + \right \rangle$?

Adjoining element in a finite field $\mathbb F_{p^n}$ to $\mathbb F_p$ to get $\mathbb F_{p^6}$

Homomorphism between the Field F and the Quotient Ring of Polynomial Ring

Field automorphisms send roots into roots

A solvable galois group implies radical extension

Understanding field automorphisms

Does it matter whether we consider field extensions as true supersets of a field?

Decomposition of Field extensions and Transcendence basis

Transcendence basis as subset of generators

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