List questions from finite-fields

Published on 18 Apr 2018 - 9:05

43

Views

Specific solutions of a random binary underdetermined linear system

Published on 25 Mar 2026 - 15:57

99

Views

If $K$ is a countable field, then $K(t_1, t_2, ..., t_n)$ is a countable field

Published on 18 Apr 2018 - 21:22

938

Views

Proof that $\Bbb{Z}_p$ is a field if $p$ is a prime (without Ring theory)

Published on 25 Mar 2026 - 13:04

73

Views

Showing a finite field isomorphism

Published on 19 Apr 2018 - 16:36

367

Views

Show $2+\alpha$ is a primitive root of $\mathbb{F}_{25}$.

Published on 25 Mar 2026 - 4:25

89

Views

Galois field over $\mathbb{Z}_{2}$.

Published on 21 Apr 2018 - 15:03

176

Views

irreducible polynomial over finite field.

Published on 25 Mar 2026 - 17:50

842

Views

Quotient ring is a field

Published on 25 Mar 2026 - 6:26

1k

Views

Finite field of with multiplication group isomorphic to the cyclic group of order $17$

Published on 23 Apr 2018 - 19:14

219

Views

Brauer group of the field of Laurent series with coefficients in a finite field

Published on 20 Mar 2026 - 8:01

65

Views

show that $x^2+x+1 \in F[x]$ is irreducible

Published on 25 Mar 2026 - 6:30

483

Views

Find all the conjugates of primitive $35th$ root of unity over $\mathbb{F_{13}}$

Published on 24 Apr 2018 - 21:15

65

Views

Every cubic extension $L/K$ is of the shape $L=K(\sqrt[3]{\alpha})$ with $\alpha$ not a cubed number and $\text{char}(K)\neq3$

Published on 25 Mar 2026 - 15:52

171

Views

The shape and group structure of an elliptic curve over $\overline{\mathbf{F}_p}$ and intermediary extensions

Published on 22 Mar 2026 - 20:46

List Question

What will be the size of this integral domain?

Specific solutions of a random binary underdetermined linear system

If $K$ is a countable field, then $K(t_1, t_2, ..., t_n)$ is a countable field

Proof that $\Bbb{Z}_p$ is a field if $p$ is a prime (without Ring theory)

Showing a finite field isomorphism

Show $2+\alpha$ is a primitive root of $\mathbb{F}_{25}$.

Galois field over $\mathbb{Z}_{2}$.

irreducible polynomial over finite field.

Quotient ring is a field

Finite field of with multiplication group isomorphic to the cyclic group of order $17$

Brauer group of the field of Laurent series with coefficients in a finite field

show that $x^2+x+1 \in F[x]$ is irreducible

Find all the conjugates of primitive $35th$ root of unity over $\mathbb{F_{13}}$

Every cubic extension $L/K$ is of the shape $L=K(\sqrt[3]{\alpha})$ with $\alpha$ not a cubed number and $\text{char}(K)\neq3$

The shape and group structure of an elliptic curve over $\overline{\mathbf{F}_p}$ and intermediary extensions

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