List questions from finite-fields

Published on 12 Apr 2026 - 3:07

329

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Linear independence over $\mathbb{F}_p$ for varying primes

Published on 17 Apr 2026 - 13:30

348

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Find a finite extension of $\mathbb F_2(x,y)$ having infinitely many intermediate subfields.

Published on 16 Apr 2026 - 13:59

211

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polynomial over a finite field

Published on 12 Apr 2026 - 20:51

185

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Structure of $C(F_5)$ from Rational Points on Elliptic Curves

Published on 13 Apr 2026 - 21:16

158

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Show a polynomial is irreducible

Published on 13 Apr 2026 - 9:07

1.2k

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Ultraproduct of the algebraic closure of finite fields

Published on 13 Apr 2026 - 18:14

754

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How many pairs of nilpotent, commuting matrices are there in $M_n(\mathbb{F}_q)$?

Published on 16 Apr 2026 - 11:34

57

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Why is it true that $F_{q^n} = F_q(\alpha)$ where $\alpha$ is the primitive element of $F_{q^n}$?

Published on 17 Apr 2026 - 15:30

612

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Count the number of rational canonical form&find similarity classess

Published on 14 Apr 2026 - 22:56

77

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If $\alpha$ = $\beta^q - \beta$ where both $\alpha$ , $\beta $ belongs to $F_q^n$ which is extension of $F_q$

Published on 16 Apr 2026 - 17:47

287

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Splitting field over $\mathbb{F}_3$

Published on 13 Apr 2026 - 14:24

2.6k

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If $F$ is a finite field then $|F|=p^n$ for prime $p$ and some integer $n$

Published on 17 Apr 2026 - 1:03

97

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Prove that $K\times K[X]/(X^7-1)\cong K\times \dots \times K$

Published on 16 Apr 2026 - 15:06

1.1k

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example of Frobenius endomorphisms that is not automorphism

Published on 14 Apr 2026 - 17:55

List Question

Well known problem about irreducibles

Linear independence over $\mathbb{F}_p$ for varying primes

Find a finite extension of $\mathbb F_2(x,y)$ having infinitely many intermediate subfields.

polynomial over a finite field

Structure of $C(F_5)$ from Rational Points on Elliptic Curves

Show a polynomial is irreducible

Ultraproduct of the algebraic closure of finite fields

How many pairs of nilpotent, commuting matrices are there in $M_n(\mathbb{F}_q)$?

Why is it true that $F_{q^n} = F_q(\alpha)$ where $\alpha$ is the primitive element of $F_{q^n}$?

Count the number of rational canonical form&find similarity classess

If $\alpha$ = $\beta^q - \beta$ where both $\alpha$ , $\beta $ belongs to $F_q^n$ which is extension of $F_q$

Splitting field over $\mathbb{F}_3$

If $F$ is a finite field then $|F|=p^n$ for prime $p$ and some integer $n$

Prove that $K\times K[X]/(X^7-1)\cong K\times \dots \times K$

example of Frobenius endomorphisms that is not automorphism

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