Question

Finite fields containing cube root of unity and square root of $-3$

score 1.7k · Answer 1 · 2018-06-18 22:50:50

1.7k

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Finite fields containing cube root of unity and square root of $-3$

Published on 18 Jun 2018 - 22:50

score 61 · Answer 2 · 2026-03-25 17:25:55

61

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Factoring polynomials: $p_2(t)=2t^4+t^2+2 \in \mathbb{Z}_3[t]$

Published on 25 Mar 2026 - 17:25

score 105 · Answer 3 · 2018-06-20 14:27:38

105

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Is $\frac{\mathbb{Z}_3[X]}{(x^2 + x + 2)}$ a field? What is the cardinality?

Published on 20 Jun 2018 - 14:27

score 1k · Answer 4 · 2018-06-21 04:04:44

1k

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Numbers of elements in field

Published on 21 Jun 2018 - 4:04

score 1.4k · Answer 5 · 2026-03-25 05:41:29

1.4k

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Primitive $p$-th root of unity with characteristic $p$

Published on 25 Mar 2026 - 5:41

score 1.9k · Answer 6 · 2018-06-22 22:20:10

1.9k

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Prove that $GL_n(\mathbb{F}_p)$ contains an element of order $p^n-1$

Published on 22 Jun 2018 - 22:20

score 1.1k · Answer 7 · 2026-03-25 12:50:52

1.1k

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Find all the monic irreducible polynomials of degree less than equal to $3$ in $F_2[X]$, and the same in $F_3[x]$.

Published on 25 Mar 2026 - 12:50

score 101 · Answer 8 · 2018-06-25 16:05:41

101

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Let's consider $\mathbb{Z}_3[x]/(x^2 + x + 2)$, I want to find solutions of $X^2 + X + 2$ in this field.

Published on 25 Jun 2018 - 16:05

score 806 · Answer 9 · 2018-06-26 14:44:52

806

Views

Roots of polynomial over finite field form a group

Published on 26 Jun 2018 - 14:44

score 257 · Answer 10 · 2018-06-27 14:19:15

257

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The order of Orthogonal group $O^{-}(2,q)$

Published on 27 Jun 2018 - 14:19

score 34 · Answer 11 · 2026-03-25 23:52:23

34

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Subfields of the finite field: Is divisibility of multiplication groups a sufficient condition?

Published on 25 Mar 2026 - 23:52

score 38 · Answer 12 · 2018-06-29 07:21:20

38

Views

is the below expression a polynomial?

Published on 29 Jun 2018 - 7:21

score 546 · Answer 13 · 2026-03-25 13:05:10

546

Views

Splitting field over a finite field

Published on 25 Mar 2026 - 13:05

score 792 · Answer 14 · 2026-03-25 13:13:31

792

Views

Galois group and intermediate subfields of finite field extension

Published on 25 Mar 2026 - 13:13

score 181 · Answer 15 · 2018-07-03 08:41:39

181

Views

On the product $\prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)$, where $p$ is prime

Published on 03 Jul 2018 - 8:41

List Question

Finite fields containing cube root of unity and square root of $-3$

Factoring polynomials: $p_2(t)=2t^4+t^2+2 \in \mathbb{Z}_3[t]$

Is $\frac{\mathbb{Z}_3[X]}{(x^2 + x + 2)}$ a field? What is the cardinality?

Numbers of elements in field

Primitive $p$-th root of unity with characteristic $p$

Prove that $GL_n(\mathbb{F}_p)$ contains an element of order $p^n-1$

Find all the monic irreducible polynomials of degree less than equal to $3$ in $F_2[X]$, and the same in $F_3[x]$.

Let's consider $\mathbb{Z}_3[x]/(x^2 + x + 2)$, I want to find solutions of $X^2 + X + 2$ in this field.

Roots of polynomial over finite field form a group

The order of Orthogonal group $O^{-}(2,q)$

Subfields of the finite field: Is divisibility of multiplication groups a sufficient condition?

is the below expression a polynomial?

Splitting field over a finite field

Galois group and intermediate subfields of finite field extension

On the product $\prod_{1\leq a<b\leq \frac{p-1}{2}}\,\left(a^2+b^2\right)$, where $p$ is prime

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