Question

Irreducibility of polynomials and its quotient

score 163 · Answer 1 · 2017-04-11 04:10:45

163

Views

Irreducibility of polynomials and its quotient

Published on 11 Apr 2017 - 4:10

score 2.1k · Answer 2 · 2017-04-11 04:33:59

2.1k

Views

Show $x^3-nx+2$ is irreducible

Published on 11 Apr 2017 - 4:33

score 1k · Answer 3 · 2017-04-11 19:50:05

1k

Views

Question about degree of a irreducible polynomial and field extensions

Published on 11 Apr 2017 - 19:50

score 95 · Answer 4 · 2017-04-12 12:26:08

95

Views

How to formally conclude that $ x^2-(\zeta_9+\zeta^{-1}_9)x+1 $ is irreducible over $\Bbb Q(\zeta_9+\zeta^{-1}_9)$

Published on 12 Apr 2017 - 12:26

score 474 · Answer 5 · 2017-04-12 14:52:26

474

Views

If $n$ is not prime, can $X^{n-1}+\dotsb+X+1$ be irreducible?

Published on 12 Apr 2017 - 14:52

score 229 · Answer 6 · 2017-04-12 17:58:01

229

Views

Reducibility of $2x^{100} +9x^5 −12x^3 +30x+15$ over $\mathbb{Q}$

Published on 12 Apr 2017 - 17:58

score 224 · Answer 7 · 2017-04-12 19:14:49

224

Views

Let $\phi : \mathbb{Q}[X] \to \mathbb{Q}[X]$ be any ring homomorphism. Prove that every irreducible factor of $\phi(f)$ has degree divisible by $n$

Published on 12 Apr 2017 - 19:14

score 1.1k · Answer 8 · 2017-04-13 07:30:17

1.1k

Views

Prove that $x^4-2x^2-11$ is irreducible over $\Bbb Q$

Published on 13 Apr 2017 - 7:30

score 152 · Answer 9 · 2017-04-13 10:56:26

152

Views

How to formally prove that the degree of $\Bbb Q（\sqrt[5]{6},\sqrt[3]{7}）$ is $15$？

Published on 13 Apr 2017 - 10:56

score 239 · Answer 10 · 2017-04-13 12:14:36

239

Views

Degree of extension $\Bbb Q(\sqrt[4]{5},\sqrt[6]{7})$.

Published on 13 Apr 2017 - 12:14

score 592 · Answer 11 · 2017-04-13 12:46:44

592

Views

Find the minimal polynomial of $\zeta_9+\zeta^{-1}_9$ over $\Bbb Q$

Published on 13 Apr 2017 - 12:46

score 1.2k · Answer 12 · 2017-04-14 16:33:36

1.2k

Views

Is irrational roots occuring in conjugate pairs valid only for Binomial surds

Published on 14 Apr 2017 - 16:33

score 85 · Answer 13 · 2017-04-14 22:16:50

85

Views

For an irreducible monic $f\in\mathbb{Z}[x]$, is it true that $\overline{f}\in\mathbb{F}_p[x]$ will be irreducible for all but finitely many $p$?

Published on 14 Apr 2017 - 22:16

score 727 · Answer 14 · 2017-04-15 17:37:27

727

Views

Find the $\text{irr}_{(\Bbb{Q(\sqrt{2}),\sqrt{2}+\sqrt{3}})}(x)$

Published on 15 Apr 2017 - 17:37

score 160 · Answer 15 · 2017-04-16 01:03:40

160

Views

Is $x^3+4$ irreducible in $Z_{11}[x]$?

Published on 16 Apr 2017 - 1:03

List Question

Irreducibility of polynomials and its quotient

Show $x^3-nx+2$ is irreducible

Question about degree of a irreducible polynomial and field extensions

How to formally conclude that $ x^2-(\zeta_9+\zeta^{-1}_9)x+1 $ is irreducible over $\Bbb Q(\zeta_9+\zeta^{-1}_9)$

If $n$ is not prime, can $X^{n-1}+\dotsb+X+1$ be irreducible?

Reducibility of $2x^{100} +9x^5 −12x^3 +30x+15$ over $\mathbb{Q}$

Let $\phi : \mathbb{Q}[X] \to \mathbb{Q}[X]$ be any ring homomorphism. Prove that every irreducible factor of $\phi(f)$ has degree divisible by $n$

Prove that $x^4-2x^2-11$ is irreducible over $\Bbb Q$

How to formally prove that the degree of $\Bbb Q（\sqrt[5]{6},\sqrt[3]{7}）$ is $15$？

Degree of extension $\Bbb Q(\sqrt[4]{5},\sqrt[6]{7})$.

Find the minimal polynomial of $\zeta_9+\zeta^{-1}_9$ over $\Bbb Q$

Is irrational roots occuring in conjugate pairs valid only for Binomial surds

For an irreducible monic $f\in\mathbb{Z}[x]$, is it true that $\overline{f}\in\mathbb{F}_p[x]$ will be irreducible for all but finitely many $p$?

Find the $\text{irr}_{(\Bbb{Q(\sqrt{2}),\sqrt{2}+\sqrt{3}})}(x)$

Is $x^3+4$ irreducible in $Z_{11}[x]$?

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