Question

Isomorphism between $K[X]/P(X)$ and $K(A)$ for $A$ a root of the irreducible polynomial $P(X)$ over $K$

score 1.2k · Answer 1 · 2026-03-26 01:23:42

1.2k

Views

Isomorphism between $K[X]/P(X)$ and $K(A)$ for $A$ a root of the irreducible polynomial $P(X)$ over $K$

Published on 26 Mar 2026 - 1:23

score 55 · Answer 2 · 2026-03-27 13:20:17

55

Views

If $L/K$ is algebraic, is $L$ a subfield of some algebraic closure $\bar K$ of $K$?

Published on 27 Mar 2026 - 13:20

score 65 · Answer 3 · 2018-10-16 21:51:59

65

Views

Field extensions confusion

Published on 16 Oct 2018 - 21:51

score 242 · Answer 4 · 2026-03-26 23:33:51

242

Views

Extending Isomorphisms

Published on 26 Mar 2026 - 23:33

score 84 · Answer 5 · 2018-10-17 11:19:04

84

Views

Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

Published on 17 Oct 2018 - 11:19

score 65 · Answer 6 · 2018-10-18 23:19:32

65

Views

"smallest" field where a polynomial is reducible

Published on 18 Oct 2018 - 23:19

score 124 · Answer 7 · 2026-03-25 12:54:07

124

Views

Classification of $\mathbb{R}/\mathbb{Q}$-forms of an algebraic group

Published on 25 Mar 2026 - 12:54

score 1.1k · Answer 8 · 2026-03-25 14:23:55

1.1k

Views

Show a regular n-sided polygon is constructible, using only ruler and compasses, iff the number $\alpha = 2 \cos(2\pi/n)$ is constructible.

Published on 25 Mar 2026 - 14:23

score 536 · Answer 9 · 2026-03-25 19:03:26

536

Views

Splitting field extension of degree $n!$

Published on 25 Mar 2026 - 19:03

score 50 · Answer 10 · 2026-03-25 01:20:38

50

Views

Is $\{sin(n \pi/2N): n\in \mathbb{Z},0<n \leq N\}$ linearly independent over $\mathbb{Q}$

Published on 25 Mar 2026 - 1:20

score 17 · Answer 11 · 2026-03-16 19:44:15

17

Views

Does co-prime and irreducibility property holds on field extensions?

Published on 16 Mar 2026 - 19:44

score 346 · Answer 12 · 2018-10-23 03:35:31

346

Views

How can I prove that $\mathbb{Q}(\sqrt[3]{2},i)=\mathbb{Q}(\sqrt[3]{2}+i)$?

Published on 23 Oct 2018 - 3:35

score 87 · Answer 13 · 2018-10-23 07:02:42

87

Views

if $\alpha$ is trascendental over K then $f(\alpha)$ is also trascendental over K?

Published on 23 Oct 2018 - 7:02

score 763 · Answer 14 · 2018-10-23 11:57:32

763

Views

Degree of the field of rational numbers extended by a complex number

Published on 23 Oct 2018 - 11:57

score 102 · Answer 15 · 2018-10-23 12:18:17

102

Views

What's the definition of nondegenerate?

Published on 23 Oct 2018 - 12:18

List Question

Isomorphism between $K[X]/P(X)$ and $K(A)$ for $A$ a root of the irreducible polynomial $P(X)$ over $K$

If $L/K$ is algebraic, is $L$ a subfield of some algebraic closure $\bar K$ of $K$?

Field extensions confusion

Extending Isomorphisms

Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

"smallest" field where a polynomial is reducible

Classification of $\mathbb{R}/\mathbb{Q}$-forms of an algebraic group

Show a regular n-sided polygon is constructible, using only ruler and compasses, iff the number $\alpha = 2 \cos(2\pi/n)$ is constructible.

Splitting field extension of degree $n!$

Is $\{sin(n \pi/2N): n\in \mathbb{Z},0<n \leq N\}$ linearly independent over $\mathbb{Q}$

Does co-prime and irreducibility property holds on field extensions?

How can I prove that $\mathbb{Q}(\sqrt[3]{2},i)=\mathbb{Q}(\sqrt[3]{2}+i)$?

if $\alpha$ is trascendental over K then $f(\alpha)$ is also trascendental over K?

Degree of the field of rational numbers extended by a complex number

What's the definition of nondegenerate?

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