List questions from field-theory

Published on 25 Mar 2026 - 1:21

93

Views

Is $[F(x) : F] = 4$ if $x$ is a root of $X^8 + 2 X^4 + 1$?

Published on 18 Jun 2018 - 21:16

1.7k

Views

Finite fields containing cube root of unity and square root of $-3$

Published on 26 Mar 2026 - 12:58

433

Views

Why is the discriminant of a number field well-defined?

Published on 23 Feb 2026 - 1:22

36

Views

About the conjugates of an element

Published on 28 Mar 2026 - 11:53

62

Views

Duality of the trace form

Published on 19 Jun 2018 - 16:28

63

Views

Concerning $\mathbb{C}(f,g)=\mathbb{C}(x,y)$

Published on 19 Jun 2018 - 19:15

270

Views

How to compute the degree of $\mathbb{Q}[\sqrt[3]{2}+\sqrt[5]{2}]$ over $\mathbb{Q}$?

Published on 28 Mar 2026 - 13:41

98

Views

Does $k(f,g)=k(h)$, where $f$ and $g$ are odd polynomials, imply that $h$ is also an odd polynomial?

Published on 20 Jun 2018 - 3:27

733

Views

Given a minimal polynomial of $a$, calculate the minimal polynomial of $a^2$

Published on 20 Jun 2018 - 12:46

106

Views

Is $\frac{\mathbb{Z}_3[X]}{(x^2 + x + 2)}$ a field? What is the cardinality?

Published on 26 Mar 2026 - 13:00

1k

Views

Numbers of elements in field

Published on 26 Mar 2026 - 12:53

161

Views

How to show that $\mathrm{Gal}(\Bbb Q(\xi_{p^n})/\Bbb Q(\xi_{p^m}))$ is cyclic?

Published on 24 Mar 2026 - 23:46

33

Views

A question about $F$-automorphism which transforms two elements.

Published on 21 Jun 2018 - 11:44

358

Views

How to show that $G=\mathrm{Gal}[\Bbb Q(\xi_{2^n})/\Bbb Q(\xi_{2^m})]$ cyclic?

Published on 28 Mar 2026 - 13:41

List Question

Should I write "a splitting field" or "the splitting field"?

Is $[F(x) : F] = 4$ if $x$ is a root of $X^8 + 2 X^4 + 1$?

Finite fields containing cube root of unity and square root of $-3$

Why is the discriminant of a number field well-defined?

About the conjugates of an element

Duality of the trace form

Concerning $\mathbb{C}(f,g)=\mathbb{C}(x,y)$

How to compute the degree of $\mathbb{Q}[\sqrt[3]{2}+\sqrt[5]{2}]$ over $\mathbb{Q}$?

Does $k(f,g)=k(h)$, where $f$ and $g$ are odd polynomials, imply that $h$ is also an odd polynomial?

Given a minimal polynomial of $a$, calculate the minimal polynomial of $a^2$

Is $\frac{\mathbb{Z}_3[X]}{(x^2 + x + 2)}$ a field? What is the cardinality?

Numbers of elements in field

How to show that $\mathrm{Gal}(\Bbb Q(\xi_{p^n})/\Bbb Q(\xi_{p^m}))$ is cyclic?

A question about $F$-automorphism which transforms two elements.

How to show that $G=\mathrm{Gal}[\Bbb Q(\xi_{2^n})/\Bbb Q(\xi_{2^m})]$ cyclic?

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