Question

Faulty proof in the claim "If a polynomial is irreducible in $Z_p [x]$ then it is irreducible in $Z_{p^k} [x]$?

score 57 · Answer 1 · 2026-03-29 10:08:47

57

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Faulty proof in the claim "If a polynomial is irreducible in $Z_p [x]$ then it is irreducible in $Z_{p^k} [x]$?

Published on 29 Mar 2026 - 10:08

score 144 · Answer 2 · 2026-04-09 00:31:51

144

Views

How can Cohn's irreducibility criterion be generalized?

Published on 09 Apr 2026 - 0:31

score 139 · Answer 3 · 2021-10-28 20:04:11

139

Views

Divisibility in $\mathbb{Q}[x]$

Published on 28 Oct 2021 - 20:04

score 205 · Answer 4 · 2026-04-11 09:45:13

205

Views

Can we prove those conjectures about a family of polynomials?

Published on 11 Apr 2026 - 9:45

score 133 · Answer 5 · 2021-10-30 10:26:10

133

Views

Minimal polynomial of $x=\sqrt{2}+i\sqrt{3}$

Published on 30 Oct 2021 - 10:26

score 159 · Answer 6 · 2026-04-03 07:57:15

159

Views

Irreducible polynomials in $\mathbb Z[X]$ with no primes in the image.

Published on 03 Apr 2026 - 7:57

score 125 · Answer 7 · 2026-03-27 17:04:23

125

Views

How to prove $X^{4}+X^{3}+X^{2}+X+1$ is irreductible in $\mathbb{F}_{2}$

Published on 27 Mar 2026 - 17:04

score 49 · Answer 8 · 2021-11-03 15:13:00

49

Views

Irreducibility of $x_1^2+x_2^2+...+x_n^2$ in $\mathbb{C}[x_1,...,x_n]$

Published on 03 Nov 2021 - 15:13

score 116 · Answer 9 · 2026-04-12 18:45:16

116

Views

In Mod p Irreducibility Test for Z[t] Need p be Prime?

Published on 12 Apr 2026 - 18:45

score 62 · Answer 10 · 2026-04-13 09:50:18

62

Views

Finding minimal polynomial of $\sqrt3 + i \sqrt 7$ over $\Bbb Q$

Published on 13 Apr 2026 - 9:50

score 197 · Answer 11 · 2021-11-07 13:41:49

197

Views

show that:this $f(x)=x^n-k$ is irreducible in $\mathbb Z[x]$

Published on 07 Nov 2021 - 13:41

score 58 · Answer 12 · 2021-11-07 18:15:52

58

Views

Irreducibility of a polynomial in $\mathbb{Q}[x,y]$

Published on 07 Nov 2021 - 18:15

score 45 · Answer 13 · 2021-11-09 09:37:08

45

Views

Whether $\mathbb{Q}[x]/(f)$ and $\mathbb{Q}[x]/(g)$ are isomorphic, with $f,g$ irreducible cubic polynomials

Published on 09 Nov 2021 - 9:37

score 70 · Answer 14 · 2021-11-11 04:05:45

70

Views

Number of roots of irreducible polynomials in extension fields

Published on 11 Nov 2021 - 4:05

score 70 · Answer 15 · 2026-04-03 03:40:32

70

Views

Factoring $t^{q^r}-t$ over the finite field $\mathbb{F}_q$

Published on 03 Apr 2026 - 3:40

List Question

Faulty proof in the claim "If a polynomial is irreducible in $Z_p [x]$ then it is irreducible in $Z_{p^k} [x]$?

How can Cohn's irreducibility criterion be generalized?

Divisibility in $\mathbb{Q}[x]$

Can we prove those conjectures about a family of polynomials?

Minimal polynomial of $x=\sqrt{2}+i\sqrt{3}$

Irreducible polynomials in $\mathbb Z[X]$ with no primes in the image.

How to prove $X^{4}+X^{3}+X^{2}+X+1$ is irreductible in $\mathbb{F}_{2}$

Irreducibility of $x_1^2+x_2^2+...+x_n^2$ in $\mathbb{C}[x_1,...,x_n]$

In Mod p Irreducibility Test for Z[t] Need p be Prime?

Finding minimal polynomial of $\sqrt3 + i \sqrt 7$ over $\Bbb Q$

show that:this $f(x)=x^n-k$ is irreducible in $\mathbb Z[x]$

Irreducibility of a polynomial in $\mathbb{Q}[x,y]$

Whether $\mathbb{Q}[x]/(f)$ and $\mathbb{Q}[x]/(g)$ are isomorphic, with $f,g$ irreducible cubic polynomials

Number of roots of irreducible polynomials in extension fields

Factoring $t^{q^r}-t$ over the finite field $\mathbb{F}_q$

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