List questions from finite-fields

Published on 25 Mar 2026 - 12:54

202

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Splitting field of the minimal polynomial

Published on 27 Mar 2026 - 21:05

342

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How to calculate the irreducible polynomial in galois field

Published on 30 Mar 2026 - 13:39

156

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How many elements of $M$ are similar to the following matrix?

Published on 26 Jun 2020 - 14:54

43

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Square values of a polynomial

Published on 27 Jun 2020 - 16:07

35

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Claim: $f(X)^{p^m}=f(X^{p^m})$, if $f(X)\in \Bbb Z_p[X]$ and $m\in \Bbb N$.

Published on 27 Jun 2020 - 20:51

110

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The roots of an irreducible polynomial over $\Bbb Z_p$ and a useful equivalence

Published on 28 Jun 2020 - 22:16

25

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Extension of $\mathbb{Q}$ by algebraic eigenvalues of commuting operators is finite

Published on 29 Jun 2020 - 2:35

47

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Polynomials of degree $n$ with $\Bbb{F}_p$ are always reducible in $\Bbb{F}_{p^n}$

Published on 29 Jun 2020 - 3:06

28

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How to get $(ab)1 = (a1)(b1)$ in Galois field?

Published on 29 Jun 2020 - 16:26

22

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Why is $\ \frac{1}{2}(p^{rmn-r})(p^r - 3)\ $ odd?

Published on 29 Jun 2020 - 16:44

30

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Show that $\psi_{b}=\psi_{c}\Leftrightarrow b=c$.

Published on 29 Jun 2020 - 19:14

287

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How to find the generators of the multiplicative group of a finite field

Published on 30 Mar 2026 - 13:41

1.2k

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What is the intuition behind mapping of elements from $GF(2^8)$ to $GF(((2^2)^2)^2)$?

Published on 29 Mar 2026 - 3:03

84

Views

Every Galois field $F$ of characteristic $p$ is perfect

Published on 30 Jun 2020 - 8:09

List Question

Equidistribution of powers of primitive roots modulo $p$

Splitting field of the minimal polynomial

How to calculate the irreducible polynomial in galois field

How many elements of $M$ are similar to the following matrix?

Square values of a polynomial

Claim: $f(X)^{p^m}=f(X^{p^m})$, if $f(X)\in \Bbb Z_p[X]$ and $m\in \Bbb N$.

The roots of an irreducible polynomial over $\Bbb Z_p$ and a useful equivalence

Extension of $\mathbb{Q}$ by algebraic eigenvalues of commuting operators is finite

Polynomials of degree $n$ with $\Bbb{F}_p$ are always reducible in $\Bbb{F}_{p^n}$

How to get $(ab)1 = (a1)(b1)$ in Galois field?

Why is $\ \frac{1}{2}(p^{rmn-r})(p^r - 3)\ $ odd?

Show that $\psi_{b}=\psi_{c}\Leftrightarrow b=c$.

How to find the generators of the multiplicative group of a finite field

What is the intuition behind mapping of elements from $GF(2^8)$ to $GF(((2^2)^2)^2)$?

Every Galois field $F$ of characteristic $p$ is perfect

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