Question

Finding the $\gcd$ of $a(x)$ and $b(x)$ in field $\mathbb{F}$

score 102 · Answer 1 · 2026-03-25 15:42:14

102

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Finding the $\gcd$ of $a(x)$ and $b(x)$ in field $\mathbb{F}$

Published on 25 Mar 2026 - 15:42

score 94 · Answer 2 · 2026-03-25 04:43:38

94

Views

Lemma 2.1 of "A SUM-PRODUCT ESTIMATE IN FINITE FIELDS, AND APPLICATION", by Bourgain, Katz and Tao

Published on 25 Mar 2026 - 4:43

score 84 · Answer 3 · 2019-01-26 17:01:02

84

Views

Linearity of the map Field Trace.

Published on 26 Jan 2019 - 17:01

score 469 · Answer 4 · 2026-03-26 02:53:47

469

Views

Verifying if a given polynomial is primitive polynomial

Published on 26 Mar 2026 - 2:53

score 1k · Answer 5 · 2026-03-26 02:55:05

1k

Views

Find the elements of the extension field using primitive polynomial over $GF(4)$

Published on 26 Mar 2026 - 2:55

score 95 · Answer 6 · 2019-01-28 05:59:18

95

Views

Determine if an ideal is a prime ideal over $\mathbb{Z}_5[x]$

Published on 28 Jan 2019 - 5:59

score 172 · Answer 7 · 2019-01-29 10:42:36

172

Views

Classify finitely-generated modules over $\mathbb{F}_2[x]/\langle x^2+x+1 \rangle$ up to isomorphism.

Published on 29 Jan 2019 - 10:42

score 161 · Answer 8 · 2026-03-25 19:32:49

161

Views

Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

Published on 25 Mar 2026 - 19:32

score 28 · Answer 9 · 2019-01-29 20:26:44

For each $k = 0, \dots, 26$ count the number of ordered pairs $(a,b)$ in $\mathbb{F}_{27} ^2$ for which $a^k = b^2$

score 392 · Answer 10 · 2026-02-23 01:25:37

392

Views

$x^2-3$ is separable over $\mathbb Q$ but not separable over $F_2$

Published on 23 Feb 2026 - 1:25

score 74 · Answer 11 · 2026-03-25 19:32:47

74

Views

The degree of a splitting field over $\mathbb{F}_p$ of non-reducible monic polynomial of degree $n$

Published on 25 Mar 2026 - 19:32

score 255 · Answer 12 · 2019-01-30 18:30:41

255

Views

Criteria when $[ML:K]= [M:K] \cdot [L:K]$ holds

Published on 30 Jan 2019 - 18:30

score 169 · Answer 13 · 2019-01-30 21:31:44

169

Views

How does a field extension maintain the field structure, and are all field extensions fields, or only algebraic extensions?

Published on 30 Jan 2019 - 21:31

score 439 · Answer 14 · 2026-03-26 06:21:01

439

Views

Factor $x^8-x$ in $\Bbb Z[x]$ and in $\Bbb Z_2[x]$

Published on 26 Mar 2026 - 6:21

score 563 · Answer 15 · 2019-02-03 10:33:50

563

Views

$\mathbb{F}_{4096}$,$\mathbb{F}_{16}$ and $\mathbb{F}_{2}$

Published on 03 Feb 2019 - 10:33

List Question

Finding the $\gcd$ of $a(x)$ and $b(x)$ in field $\mathbb{F}$

Lemma 2.1 of "A SUM-PRODUCT ESTIMATE IN FINITE FIELDS, AND APPLICATION", by Bourgain, Katz and Tao

Linearity of the map Field Trace.

Verifying if a given polynomial is primitive polynomial

Find the elements of the extension field using primitive polynomial over $GF(4)$

Determine if an ideal is a prime ideal over $\mathbb{Z}_5[x]$

Classify finitely-generated modules over $\mathbb{F}_2[x]/\langle x^2+x+1 \rangle$ up to isomorphism.

Splitting field of an irreductible polynomial $f(X) \in F_{q}[X]$

For each $k = 0, \dots, 26$ count the number of ordered pairs $(a,b)$ in $\mathbb{F}_{27} ^2$ for which $a^k = b^2$

$x^2-3$ is separable over $\mathbb Q$ but not separable over $F_2$

The degree of a splitting field over $\mathbb{F}_p$ of non-reducible monic polynomial of degree $n$

Criteria when $[ML:K]= [M:K] \cdot [L:K]$ holds

How does a field extension maintain the field structure, and are all field extensions fields, or only algebraic extensions?

Factor $x^8-x$ in $\Bbb Z[x]$ and in $\Bbb Z_2[x]$

$\mathbb{F}_{4096}$,$\mathbb{F}_{16}$ and $\mathbb{F}_{2}$

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