Question

Show $\mathbb Z[x] / I \cong \overline{\mathbb Z}[x]/ \overline{I}$ where $\overline{\mathbb Z} = (\mathbb Z /3 \mathbb Z)$

score 84 · Answer 1 · 2026-03-27 07:18:53

84

Views

Show $\mathbb Z[x] / I \cong \overline{\mathbb Z}[x]/ \overline{I}$ where $\overline{\mathbb Z} = (\mathbb Z /3 \mathbb Z)$

Published on 27 Mar 2026 - 7:18

score 817 · Answer 2 · 2019-07-14 15:41:30

817

Views

Understanding the formula:$ [GF(p^n):GF(p)]=n$

Published on 14 Jul 2019 - 15:41

score 118 · Answer 3 · 2019-07-15 14:30:33

118

Views

Proving that multiplicative groups of two fields F* are isomorphic

Published on 15 Jul 2019 - 14:30

score 112 · Answer 4 · 2019-07-17 06:43:27

112

Views

Over $\mathbb{F}_2$, find a $5\times 5$ matrix of order 31.

Published on 17 Jul 2019 - 6:43

score 71 · Answer 5 · 2026-03-28 04:34:54

71

Views

Find a field extension $E/\mathbb{F}_7$ of degree $3$

Published on 28 Mar 2026 - 4:34

score 35 · Answer 6 · 2019-07-20 08:58:55

35

Views

Question about automorphism of finite field

Published on 20 Jul 2019 - 8:58

score 875 · Answer 7 · 2026-03-25 23:51:46

875

Views

Splitting Field of $x^4 + x^3 + 1$ over $\mathbb{F}_{32}$

Published on 25 Mar 2026 - 23:51

score 448 · Answer 8 · 2026-03-27 07:16:59

448

Views

Prove that there exists an irreducible polynomial $f\in\mathbb{F}_p[x]$ of degree $2014$

Published on 27 Mar 2026 - 7:16

score 207 · Answer 9 · 2019-07-24 00:44:55

207

Views

Does the fiber cardinality increase under specialization over a finite field?

Published on 24 Jul 2019 - 0:44

score 223 · Answer 10 · 2019-07-24 14:57:05

223

Views

Vandermonde determinant of the elements of a finite field

Published on 24 Jul 2019 - 14:57

score 235 · Answer 11 · 2019-07-24 20:33:46

235

Views

Show that if $m$ is prime then the product of two non-zero elements of $\mathbb Z/m\mathbb Z$ is again non-zero

Published on 24 Jul 2019 - 20:33

score 46 · Answer 12 · 2026-03-27 16:22:02

46

Views

Does this hold anywhere close to remotely over finite fields and rings?

Published on 27 Mar 2026 - 16:22

score 179 · Answer 13 · 2019-07-25 14:29:59

179

Views

Field with $p^2$ elements where $p \equiv 3 \pmod 4$ is a prime number

Published on 25 Jul 2019 - 14:29

score 420 · Answer 14 · 2019-07-25 20:23:33

420

Views

Prove that the number of $\alpha\in\mathbb{F}_{27}$ such that $|A_\alpha|=26 $ equals 12.

Published on 25 Jul 2019 - 20:23

score 71 · Answer 15 · 2019-07-25 23:17:50

71

Views

Is the finite field $Z_p$ an ordered one? Or can a finite field be ordered?

Published on 25 Jul 2019 - 23:17

List Question

Show $\mathbb Z[x] / I \cong \overline{\mathbb Z}[x]/ \overline{I}$ where $\overline{\mathbb Z} = (\mathbb Z /3 \mathbb Z)$

Understanding the formula:$ [GF(p^n):GF(p)]=n$

Proving that multiplicative groups of two fields F* are isomorphic

Over $\mathbb{F}_2$, find a $5\times 5$ matrix of order 31.

Find a field extension $E/\mathbb{F}_7$ of degree $3$

Question about automorphism of finite field

Splitting Field of $x^4 + x^3 + 1$ over $\mathbb{F}_{32}$

Prove that there exists an irreducible polynomial $f\in\mathbb{F}_p[x]$ of degree $2014$

Does the fiber cardinality increase under specialization over a finite field?

Vandermonde determinant of the elements of a finite field

Show that if $m$ is prime then the product of two non-zero elements of $\mathbb Z/m\mathbb Z$ is again non-zero

Does this hold anywhere close to remotely over finite fields and rings?

Field with $p^2$ elements where $p \equiv 3 \pmod 4$ is a prime number

Prove that the number of $\alpha\in\mathbb{F}_{27}$ such that $|A_\alpha|=26 $ equals 12.

Is the finite field $Z_p$ an ordered one? Or can a finite field be ordered?

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