List questions from field-theory

Published on 25 Mar 2026 - 9:27

140

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Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

Published on 25 Mar 2026 - 9:49

167

Views

About number of algebra of dimension 2 over a field

Published on 25 Mar 2026 - 11:06

503

Views

Galois extension from $GF(5)$ to $GF(25)$.

Published on 25 Mar 2026 - 20:52

388

Views

Completeness in Levi-Civita field

Published on 25 Mar 2026 - 23:06

268

Views

Calculate the square root of a number in $\mathbb{Q}(\sqrt[3]{7})$

Published on 25 Mar 2026 - 9:27

513

Views

Splitting field of $X^5-t$ in $\mathbb{Q}(t)[X]$

Published on 27 Mar 2026 - 0:37

44

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On a characterization of a field monomorphism

Published on 27 Mar 2026 - 2:23

2.8k

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For ring homomorphism $\phi:R\to S$, prove that if $R$ is a field and $\phi(R)\neq \left \{0_{S} \right \}$, then $\phi(R)$ is a field.

Published on 24 Mar 2026 - 23:49

1.9k

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Show that $\Bbb F_2[x]/(x^3+x+1)$ is a field and more...

Published on 25 Mar 2026 - 22:30

239

Views

For a finite extension $K/F$ of degree $>1$, prove that $K$ is not the union of finitely many proper intermediate fields.

Published on 25 Mar 2026 - 10:58

34

Views

$k$ be an algebraically closed field , $R=M(n,k)$ , then $k \cong End_R (k^n)$

Published on 24 Mar 2026 - 23:48

53

Views

Degree of Extensions

Published on 25 Mar 2026 - 10:52

47

Views

Characteristic fields and extensions

Published on 25 Mar 2026 - 12:13

602

Views

Proving $Gal(K/\mathbb{Q})$ is $D_4$.

Published on 25 Mar 2026 - 9:47

List Question

confused about $\Bbb F_3(\alpha) \cong \Bbb F_3/\langle x^3+2x+2\rangle$

Find a splitting field for $f(x) = x^6 − 2 $ over $GF(7)$ .

About number of algebra of dimension 2 over a field

Galois extension from $GF(5)$ to $GF(25)$.

Completeness in Levi-Civita field

Calculate the square root of a number in $\mathbb{Q}(\sqrt[3]{7})$

Splitting field of $X^5-t$ in $\mathbb{Q}(t)[X]$

On a characterization of a field monomorphism

For ring homomorphism $\phi:R\to S$, prove that if $R$ is a field and $\phi(R)\neq \left \{0_{S} \right \}$, then $\phi(R)$ is a field.

Show that $\Bbb F_2[x]/(x^3+x+1)$ is a field and more...

For a finite extension $K/F$ of degree $>1$, prove that $K$ is not the union of finitely many proper intermediate fields.

$k$ be an algebraically closed field , $R=M(n,k)$ , then $k \cong End_R (k^n)$

Degree of Extensions

Characteristic fields and extensions

Proving $Gal(K/\mathbb{Q})$ is $D_4$.

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