Question

Monic irreducible polynomial $f \in \mathbb{Z}[x]$ of degree $n$ such that $\operatorname{Gal}(f) \cap C_j \neq \emptyset$ $ \forall j$…

score 109 · Answer 1 · 2026-04-03 14:57:29

109

Views

Monic irreducible polynomial $f \in \mathbb{Z}[x]$ of degree $n$ such that $\operatorname{Gal}(f) \cap C_j \neq \emptyset$ $ \forall j$…

Published on 03 Apr 2026 - 14:57

score 176 · Answer 2 · 2026-03-29 14:20:02

176

Views

"Low degree Polynomials do not have too many roots" - what exactly does this mean?

Published on 29 Mar 2026 - 14:20

score 50 · Answer 3 · 2026-04-03 15:23:01

50

Views

Show $\mathbb{F}_p(b)=\mathbb{F}_{p^{pk}}$ where $1/(1-b)$ is a root of $x^p-x-a^{-1}$

Published on 03 Apr 2026 - 15:23

score 147 · Answer 4 · 2023-06-26 15:55:09

147

Views

What is $\{u+u^p: u\in F\}$ in the finite field $F_{p^n}$?

Published on 26 Jun 2023 - 15:55

score 59 · Answer 5 · 2026-03-29 07:32:55

59

Views

Describe the Galois group of a cubic and quartic over $\mathbb{F}_p(y)$

Published on 29 Mar 2026 - 7:32

score 90 · Answer 6 · 2023-06-28 17:55:17

90

Views

Can a basis together with the zero vector form a vector space?

Published on 28 Jun 2023 - 17:55

score 63 · Answer 7 · 2023-06-30 08:46:28

63

Views

Arithmetic in the finite field $\mathbb{F}_{2^4}$

Published on 30 Jun 2023 - 8:46

score 130 · Answer 8 · 2026-04-03 14:53:13

130

Views

What are elements of the field $\frac{\mathbb{F}_2[x,y]}{x^3-y^2+x+1}$? Is that polynomial irreducible?

Published on 03 Apr 2026 - 14:53

score 52 · Answer 9 · 2026-04-05 04:51:14

52

Views

Sum of tensor products as tensor products

Published on 05 Apr 2026 - 4:51

score 70 · Answer 10 · 2023-07-05 20:27:50

70

Views

$F$ is a finite field whose order is a power of 3, then $\sqrt{-1} \in F$ if and only if $\sqrt[4]{-1} \in F$

Published on 05 Jul 2023 - 20:27

score 52 · Answer 11 · 2023-07-05 21:32:37

52

Views

Question regarding a cyclic field extension over a field of positive characteristic.

Published on 05 Jul 2023 - 21:32

score 52 · Answer 12 · 2023-07-06 14:39:35

52

Views

Products of permutation and diagonal matrices over finite fields

Published on 06 Jul 2023 - 14:39

score 88 · Answer 13 · 2026-03-29 17:07:12

88

Views

Using Chinese Remainder theorem to find number of solutions of modular exponentiation mod composite number

Published on 29 Mar 2026 - 17:07

score 69 · Answer 14 · 2026-03-29 05:42:29

69

Views

Find basis vectors with fewest nonzero entries

Published on 29 Mar 2026 - 5:42

score 70 · Answer 15 · 2026-04-04 03:29:49

70

Views

How many linear transformations from $F$ into $K$?

Published on 04 Apr 2026 - 3:29

List Question

Monic irreducible polynomial $f \in \mathbb{Z}[x]$ of degree $n$ such that $\operatorname{Gal}(f) \cap C_j \neq \emptyset$ $ \forall j$…

"Low degree Polynomials do not have too many roots" - what exactly does this mean?

Show $\mathbb{F}_p(b)=\mathbb{F}_{p^{pk}}$ where $1/(1-b)$ is a root of $x^p-x-a^{-1}$

What is $\{u+u^p: u\in F\}$ in the finite field $F_{p^n}$?

Describe the Galois group of a cubic and quartic over $\mathbb{F}_p(y)$

Can a basis together with the zero vector form a vector space?

Arithmetic in the finite field $\mathbb{F}_{2^4}$

What are elements of the field $\frac{\mathbb{F}_2[x,y]}{x^3-y^2+x+1}$? Is that polynomial irreducible?

Sum of tensor products as tensor products

$F$ is a finite field whose order is a power of 3, then $\sqrt{-1} \in F$ if and only if $\sqrt[4]{-1} \in F$

Question regarding a cyclic field extension over a field of positive characteristic.

Products of permutation and diagonal matrices over finite fields

Using Chinese Remainder theorem to find number of solutions of modular exponentiation mod composite number

Find basis vectors with fewest nonzero entries

How many linear transformations from $F$ into $K$?

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