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Question regarding $K(a) \cong K[X]/(m(a,K))$ and the representation of elements in $L$ as linear combination

score 33 · Answer 1 · 2026-04-13 22:34:56

33

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Question regarding $K(a) \cong K[X]/(m(a,K))$ and the representation of elements in $L$ as linear combination

Published on 13 Apr 2026 - 22:34

score 74 · Answer 2 · 2026-04-10 01:54:06

74

Views

Algebraic closure à la Artin -- the ideal in the construction is not maximal?

Published on 10 Apr 2026 - 1:54

score 82 · Answer 3 · 2026-05-11 09:36:24

82

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A field has a unique algebraic extension of each degree if and only if its absolute Galois group is the profinite completion of integers

Published on 11 May 2026 - 9:36

score 55 · Answer 4 · 2026-04-09 18:13:10

55

Views

Specific example of fixed field using Artin's Theorem

Published on 09 Apr 2026 - 18:13

score 65 · Answer 5 · 2026-05-14 17:28:51

65

Views

Separable extension characterization

Published on 14 May 2026 - 17:28

score 44 · Answer 6 · 2026-04-11 00:02:57

44

Views

Question about Splitting Field Extensions

Published on 11 Apr 2026 - 0:02

score 87 · Answer 7 · 2026-04-13 17:49:16

87

Views

Why is this argument used to explain that natural numbers are assumed to be non-zero?

Published on 13 Apr 2026 - 17:49

score 80 · Answer 8 · 2026-04-13 19:07:25

80

Views

Injectivity preservation for polynomial maps under field extension

Published on 13 Apr 2026 - 19:07

score 35 · Answer 9 · 2026-04-14 08:36:33

35

Views

Solution to the Integral of the Multiplication of Two Polynomials Under the Square Root

Published on 14 Apr 2026 - 8:36

score 36 · Answer 10 · 2026-04-15 10:45:09

36

Views

A question from Dummit-Foote on showing nontrivial algebraic extensions of a certain field (Section 14.9, Q.15)

Published on 15 Apr 2026 - 10:45

score 69 · Answer 11 · 2026-04-15 06:56:53

69

Views

$\mathbb Q$ is the only infinite prime field

Published on 15 Apr 2026 - 6:56

score 65 · Answer 12 · 2026-04-12 12:02:19

65

Views

Ring $A$ with $4$ elements

Published on 12 Apr 2026 - 12:02

score 64 · Answer 13 · 2026-04-09 15:24:37

64

Views

Are all algebraic extensions of finite fields separable? What about fields of characteristic p in general?

Published on 09 Apr 2026 - 15:24

score 89 · Answer 14 · 2026-04-11 22:05:08

89

Views

On the definition of algebraic closure

Published on 11 Apr 2026 - 22:05

score 117 · Answer 15 · 2026-04-14 14:06:10

117

Views

Minimal Polynomial of $\sqrt[3]{2}$ over $\mathbb{Q}(e^{\frac{2\pi i}{3}})$ and degree of field extension.

Published on 14 Apr 2026 - 14:06

List Question

Question regarding $K(a) \cong K[X]/(m(a,K))$ and the representation of elements in $L$ as linear combination

Algebraic closure à la Artin -- the ideal in the construction is not maximal?

A field has a unique algebraic extension of each degree if and only if its absolute Galois group is the profinite completion of integers

Specific example of fixed field using Artin's Theorem

Separable extension characterization

Question about Splitting Field Extensions

Why is this argument used to explain that natural numbers are assumed to be non-zero?

Injectivity preservation for polynomial maps under field extension

Solution to the Integral of the Multiplication of Two Polynomials Under the Square Root

A question from Dummit-Foote on showing nontrivial algebraic extensions of a certain field (Section 14.9, Q.15)

$\mathbb Q$ is the only infinite prime field

Ring $A$ with $4$ elements

Are all algebraic extensions of finite fields separable? What about fields of characteristic p in general?

On the definition of algebraic closure

Minimal Polynomial of $\sqrt[3]{2}$ over $\mathbb{Q}(e^{\frac{2\pi i}{3}})$ and degree of field extension.

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