Question

Closure property of a field

score 1k · Answer 1 · 2019-09-18 15:37:35

1k

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Closure property of a field

Published on 18 Sep 2019 - 15:37

score 699 · Answer 2 · 2026-03-26 19:00:42

699

Views

galois field convert element in GF($2^8$) to form a+bt

Published on 26 Mar 2026 - 19:00

score 64 · Answer 3 · 2019-09-19 13:27:46

64

Views

To obtain the elementary symmetric polynomial in the binary finite field

Published on 19 Sep 2019 - 13:27

score 178 · Answer 4 · 2019-09-20 07:12:08

178

Views

How many different solutions does $x^2_{1}+2x^2_{2}+3x^3_{3}=4x^2_{4} $ have?

Published on 20 Sep 2019 - 7:12

score 91 · Answer 5 · 2019-09-20 21:17:26

91

Views

Finding the algebraic elements of $\mathbb{F}_3(x,y)$ over $\mathbb{F}_3$, where $y^2+x^4-x^2+1=0$.

Published on 20 Sep 2019 - 21:17

score 511 · Answer 6 · 2026-03-28 06:59:46

511

Views

The structure of the unit circle in the plane $F^2$, where $F$ is a finite field with odd characteristic.

Published on 28 Mar 2026 - 6:59

score 266 · Answer 7 · 2026-03-26 19:01:53

266

Views

Definition of the multiplication matrix of element of finite field.

Published on 26 Mar 2026 - 19:01

score 533 · Answer 8 · 2026-03-26 21:26:00

533

Views

roots of unity in finite fields from complex roots of unity

Published on 26 Mar 2026 - 21:26

score 42 · Answer 9 · 2019-09-25 02:31:53

42

Views

When making a finite field from an irreducible polynomial, is the degree the only relevant property?

Published on 25 Sep 2019 - 2:31

score 117 · Answer 10 · 2019-09-25 17:03:13

117

Views

For any prime number $p$ and $m \in \Bbb N$ there exists a field of cardinality $p^m.$

Published on 25 Sep 2019 - 17:03

score 281 · Answer 11 · 2026-03-27 15:07:22

281

Views

A curious condition for $f$ being irreducible in $\mathbb{Q}$[x]

Published on 27 Mar 2026 - 15:07

score 59 · Answer 12 · 2019-09-27 19:00:11

59

Views

common roots of polynomials in Galois fields and the complex numbers

Published on 27 Sep 2019 - 19:00

score 130 · Answer 13 · 2026-03-27 15:05:37

130

Views

If $p$ prime, $a∈\mathbb{Z}$ , $n∈\mathbb{N}$, $g∈\mathbb{Z} [x]$, deg $g < n$, $p \nmid g(a)$ then $(x − a)^n + p · g(x)$ irred. $\mathbb{Q}[x]$

Published on 27 Mar 2026 - 15:05

score 83 · Answer 14 · 2019-09-30 11:06:30

83

Views

Rational canonical form of a matrix $M \in GL(n,\mathbb{F}_2)$.

Published on 30 Sep 2019 - 11:06

score 87 · Answer 15 · 2026-03-27 14:59:07

87

Views

How to prove how many ireducible polynomials are in a polynomial ring over a finite field.

Published on 27 Mar 2026 - 14:59

List Question

Closure property of a field

galois field convert element in GF($2^8$) to form a+bt

To obtain the elementary symmetric polynomial in the binary finite field

How many different solutions does $x^2_{1}+2x^2_{2}+3x^3_{3}=4x^2_{4} $ have?

Finding the algebraic elements of $\mathbb{F}_3(x,y)$ over $\mathbb{F}_3$, where $y^2+x^4-x^2+1=0$.

The structure of the unit circle in the plane $F^2$, where $F$ is a finite field with odd characteristic.

Definition of the multiplication matrix of element of finite field.

roots of unity in finite fields from complex roots of unity

When making a finite field from an irreducible polynomial, is the degree the only relevant property?

For any prime number $p$ and $m \in \Bbb N$ there exists a field of cardinality $p^m.$

A curious condition for $f$ being irreducible in $\mathbb{Q}$[x]

common roots of polynomials in Galois fields and the complex numbers

If $p$ prime, $a∈\mathbb{Z}$ , $n∈\mathbb{N}$, $g∈\mathbb{Z} [x]$, deg $g < n$, $p \nmid g(a)$ then $(x − a)^n + p · g(x)$ irred. $\mathbb{Q}[x]$

Rational canonical form of a matrix $M \in GL(n,\mathbb{F}_2)$.

How to prove how many ireducible polynomials are in a polynomial ring over a finite field.

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