Question

The discriminant and Stickelberger's Theorem

score 141 · Answer 1 · 2022-05-04 11:53:42

141

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The discriminant and Stickelberger's Theorem

Published on 04 May 2022 - 11:53

score 66 · Answer 2 · 2022-05-08 07:47:48

66

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Degree of elements in simple extension of $\mathbb{Q}$

Published on 08 May 2022 - 7:47

score 56 · Answer 3 · 2022-06-01 17:24:19

56

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Is there a standard way of writing constructible numbers?

Published on 01 Jun 2022 - 17:24

score 45 · Answer 4 · 2022-06-06 13:57:55

45

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Squares in Algebraic Extensions

Published on 06 Jun 2022 - 13:57

score 67 · Answer 5 · 2022-06-16 06:54:28

67

Views

A question on the definition of algebraic

Published on 16 Jun 2022 - 6:54

score 75 · Answer 6 · 2022-06-21 12:04:48

75

Views

Let $K/F$ and $a,b \in K$ algebraic over $F$ and $[F(a):F]=m ,[F(b):F]=n$ then show that degree of $a + b, ab, a − b , ab^{−1}$ atmost $mn$ over $F$

Published on 21 Jun 2022 - 12:04

score 314 · Answer 7 · 2022-06-22 06:07:59

314

Views

$F(\alpha)$ is isomorphic to the field $F(x)$ of rational functions over $F$ in the indeterminate $x$ where $\alpha$ is transcendental over $F$

Published on 22 Jun 2022 - 6:07

score 153 · Answer 8 · 2022-06-22 07:46:32

153

Views

If $\alpha ,\beta$ algebraic over $F$ then there exist a isomorphism $\psi:F(\alpha) \to F(\beta) $iff $\alpha,\beta$ have same minimal polynomial

Published on 22 Jun 2022 - 7:46

score 44 · Answer 9 · 2022-07-05 20:25:04

44

Views

Algebraic independence of a family of numbers

Published on 05 Jul 2022 - 20:25

score 204 · Answer 10 · 2022-07-13 15:41:39

204

Views

Is every element of GF(p^k) whose degree is k a generator?

Published on 13 Jul 2022 - 15:41

score 122 · Answer 11 · 2022-07-30 07:29:47

122

Views

Degree of $\sqrt[5]{2+\sqrt[3]{5+\sqrt{2}}} \cdot e^{2\pi i /3}$ as algebraic number

Published on 30 Jul 2022 - 7:29

score 93 · Answer 12 · 2022-08-03 19:07:07

93

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Problem in trigonometry solved with more advanced topics - $\displaystyle \cos(q\pi) \in \mathbb{Q} \to \cos(q\pi) \in \{0, \pm \frac{1}{2}, \pm 1\}$

Published on 03 Aug 2022 - 19:07

score 136 · Answer 13 · 2026-02-23 06:01:55

136

Views

Understanding Liouville numbers and irrationality measure

Published on 23 Feb 2026 - 6:01

score 144 · Answer 14 · 2022-08-08 20:23:47

144

Views

What gives the golden ratio its unusual numerical properties?

Published on 08 Aug 2022 - 20:23

score 93 · Answer 15 · 2022-08-25 07:18:58

Is my solution ok? The set of the algebraic numbers obtained as roots of polynomials with integer coefficients that have degree $n$ is countable.

List Question

The discriminant and Stickelberger's Theorem

Degree of elements in simple extension of $\mathbb{Q}$

Is there a standard way of writing constructible numbers?

Squares in Algebraic Extensions

A question on the definition of algebraic

Let $K/F$ and $a,b \in K$ algebraic over $F$ and $[F(a):F]=m ,[F(b):F]=n$ then show that degree of $a + b, ab, a − b , ab^{−1}$ atmost $mn$ over $F$

$F(\alpha)$ is isomorphic to the field $F(x)$ of rational functions over $F$ in the indeterminate $x$ where $\alpha$ is transcendental over $F$

If $\alpha ,\beta$ algebraic over $F$ then there exist a isomorphism $\psi:F(\alpha) \to F(\beta) $iff $\alpha,\beta$ have same minimal polynomial

Algebraic independence of a family of numbers

Is every element of GF(p^k) whose degree is k a generator?

Degree of $\sqrt[5]{2+\sqrt[3]{5+\sqrt{2}}} \cdot e^{2\pi i /3}$ as algebraic number

Problem in trigonometry solved with more advanced topics - $\displaystyle \cos(q\pi) \in \mathbb{Q} \to \cos(q\pi) \in \{0, \pm \frac{1}{2}, \pm 1\}$

Understanding Liouville numbers and irrationality measure

What gives the golden ratio its unusual numerical properties?

Is my solution ok? The set of the algebraic numbers obtained as roots of polynomials with integer coefficients that have degree $n$ is countable.

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