List questions from finite-fields

Published on 07 Jan 2020 - 4:42

816

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primitive element $\alpha$ in $\mathbb{F}_{25}$

Published on 07 Jan 2020 - 9:26

69

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definition of the trace by conjugates and using the characteristic polynomial

Published on 20 Mar 2026 - 7:41

705

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Square root of matrix over $F_p$

Published on 29 Mar 2026 - 11:43

107

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Rank and determinant of matrices over $\mathbb{Z}/p\mathbb{Z}$

Published on 07 Jan 2020 - 18:29

63

Views

Splitting Field of $(x^3-2)(x^2-2)$ over $\mathbb{F}_3$ and its degree

Published on 26 Mar 2026 - 11:18

59

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Easy proof of the existence of a primitive element in a finite field

Published on 09 Jan 2020 - 15:36

185

Views

What is an Omega group on a finite field?

Published on 10 Jan 2020 - 11:26

1.4k

Views

Frobenius Mapping as a Ring Homomorphism

Published on 23 Feb 2026 - 6:16

97

Views

Element of order $7$ in $GL(4,2)$

Published on 11 Jan 2020 - 7:23

77

Views

Is $K = \bigcup\limits_{i:\text{even}} \mathbb{F_{2^i}}$ a field?

Published on 11 Jan 2020 - 20:10

67

Views

Linear equation system over field $\mathbb{Z}/3\mathbb{Z}$

Published on 12 Jan 2020 - 12:49

285

Views

Let $f ∈ \mathbb{F}_p[x]$ be an irreducible polynomial. Show that $f$ splits into linear factors in $\mathbb{F}_{p^{\deg(f)}}$.

Published on 26 Mar 2026 - 14:34

99

Views

properties of the Galois field and cyclic group

Published on 29 Mar 2026 - 21:55

243

Views

Galois Field of order $p^n$ as a vector space over Galois Field of order $p$

Published on 13 Jan 2020 - 18:53

List Question

Roots of irreducible polynomial over finite field extension.

primitive element $\alpha$ in $\mathbb{F}_{25}$

definition of the trace by conjugates and using the characteristic polynomial

Square root of matrix over $F_p$

Rank and determinant of matrices over $\mathbb{Z}/p\mathbb{Z}$

Splitting Field of $(x^3-2)(x^2-2)$ over $\mathbb{F}_3$ and its degree

Easy proof of the existence of a primitive element in a finite field

What is an Omega group on a finite field?

Frobenius Mapping as a Ring Homomorphism

Element of order $7$ in $GL(4,2)$

Is $K = \bigcup\limits_{i:\text{even}} \mathbb{F_{2^i}}$ a field?

Linear equation system over field $\mathbb{Z}/3\mathbb{Z}$

Let $f ∈ \mathbb{F}_p[x]$ be an irreducible polynomial. Show that $f$ splits into linear factors in $\mathbb{F}_{p^{\deg(f)}}$.

properties of the Galois field and cyclic group

Galois Field of order $p^n$ as a vector space over Galois Field of order $p$

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