Question

Let $f(x) \in F[x]$ be irreducible (F is a Field). Suppose $f(x) \mid g_1(x)g_2(x)\dots g_k(x)$

score 77 · Answer 1 · 2015-11-07 22:05:51

77

Views

Let $f(x) \in F[x]$ be irreducible (F is a Field). Suppose $f(x) \mid g_1(x)g_2(x)\dots g_k(x)$

Published on 07 Nov 2015 - 22:05

score 300 · Answer 2 · 2026-03-27 02:40:30

300

Views

Irreducibility, Cyclotomic polynomial, How do Binomial Coefficients Simplify?

Published on 27 Mar 2026 - 2:40

score 333 · Answer 3 · 2026-03-30 17:09:42

333

Views

Irreducibility of $x^3 − a$ over the field of $q$ elements

Published on 30 Mar 2026 - 17:09

score 549 · Answer 4 · 2015-11-11 05:01:50

549

Views

If $f$ and $g$ are independent polynomials and $h$ is a nonzero polynomial, then $fh$ and $gh$ are independent

Published on 11 Nov 2015 - 5:01

score 645 · Answer 5 · 2015-11-11 18:19:15

645

Views

Showing a Polynomial is Irreducible in Z8

Published on 11 Nov 2015 - 18:19

score 148 · Answer 6 · 2015-11-14 06:49:56

148

Views

irreducibility of a polynomial over $\mathbb{F}_2$

Published on 14 Nov 2015 - 6:49

score 256 · Answer 7 · 2015-11-14 07:11:03

256

Views

Is there any algorithm that produces irreducible polynomials over $\mathbb{F}_2$?

Published on 14 Nov 2015 - 7:11

score 236 · Answer 8 · 2015-11-14 14:26:30

236

Views

Why $3X^3+12X^2+30$ is irreducible on $\mathbb Q$ and not in $\mathbb Z$?

Published on 14 Nov 2015 - 14:26

score 1k · Answer 9 · 2015-11-16 13:23:49

1k

Views

$X^p-t\in\mathbb F_p(t)[X]$ is irreducible but has one root.

Published on 16 Nov 2015 - 13:23

score 73 · Answer 10 · 2015-11-16 23:19:16

73

Views

What would the factored form of a square root?

Published on 16 Nov 2015 - 23:19

score 22 · Answer 11 · 2026-03-18 23:56:43

22

Views

If $P\in K[X]$ irreducible, and if $\alpha_1,...,\alpha_n$ are his roots, does his splitting field is $K(\alpha_1,...,\alpha_n)$?

Published on 18 Mar 2026 - 23:56

score 228 · Answer 12 · 2015-11-18 02:07:56

228

Views

Let $f(x)=x^7-7x+3\in{Q[x]}$, show that $f(x)$ is irreducible over $Q$

Published on 18 Nov 2015 - 2:07

score 63 · Answer 13 · 2015-11-18 13:42:43

63

Views

Factoring/Reducing a polynomial $x^4 -2x^3 + 2x^2 + x + 4$

Published on 18 Nov 2015 - 13:42

score 151 · Answer 14 · 2026-04-04 17:30:20

151

Views

Is "to be conjugate" is an equivalence relation?

Published on 04 Apr 2026 - 17:30

score 36 · Answer 15 · 2015-11-20 19:31:21

36

Views

Construct $K=\{ (a+bi)+(c+di)\sqrt{2} \}$ with Extension Fields

Published on 20 Nov 2015 - 19:31

List Question

Let $f(x) \in F[x]$ be irreducible (F is a Field). Suppose $f(x) \mid g_1(x)g_2(x)\dots g_k(x)$

Irreducibility, Cyclotomic polynomial, How do Binomial Coefficients Simplify?

Irreducibility of $x^3 − a$ over the field of $q$ elements

If $f$ and $g$ are independent polynomials and $h$ is a nonzero polynomial, then $fh$ and $gh$ are independent

Showing a Polynomial is Irreducible in Z8

irreducibility of a polynomial over $\mathbb{F}_2$

Is there any algorithm that produces irreducible polynomials over $\mathbb{F}_2$?

Why $3X^3+12X^2+30$ is irreducible on $\mathbb Q$ and not in $\mathbb Z$?

$X^p-t\in\mathbb F_p(t)[X]$ is irreducible but has one root.

What would the factored form of a square root?

If $P\in K[X]$ irreducible, and if $\alpha_1,...,\alpha_n$ are his roots, does his splitting field is $K(\alpha_1,...,\alpha_n)$?

Let $f(x)=x^7-7x+3\in{Q[x]}$, show that $f(x)$ is irreducible over $Q$

Factoring/Reducing a polynomial $x^4 -2x^3 + 2x^2 + x + 4$

Is "to be conjugate" is an equivalence relation?

Construct $K=\{ (a+bi)+(c+di)\sqrt{2} \}$ with Extension Fields

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