Question

Equivalent definition of a perfect field

score 27 · Answer 1 · 2026-02-23 12:02:58

27

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Equivalent definition of a perfect field

Published on 23 Feb 2026 - 12:02

score 34 · Answer 2 · 2026-02-23 12:08:49

34

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$L/K$ be a field extension with $Char(K) = p > 0$ and $[L : K] = n$ cannot be divided by $p$. Show that $L/K$ is separable.

Published on 23 Feb 2026 - 12:08

score 134 · Answer 3 · 2024-03-15 06:25:34

134

Views

Are two principal ideals are equal if their generator has the same root in some extension?

Published on 15 Mar 2024 - 6:25

score 232 · Answer 4 · 2024-03-17 04:45:39

232

Views

Irreducibility of the polynomial $x^n+5x+3$ over $\mathbb{Q}$

Published on 17 Mar 2024 - 4:45

score 220 · Answer 5 · 2026-03-26 16:05:39

220

Views

Fifth cyclotomic polynomial over a finite field

Published on 26 Mar 2026 - 16:05

score 59 · Answer 6 · 2024-03-19 10:26:57

59

Views

Decomposition of a polynomial of the form $X^{p^n}-X$ in finite fields.

Published on 19 Mar 2024 - 10:26

score 57 · Answer 7 · 2024-03-21 04:43:10

57

Views

If $p(x) = a_3 + a_2x + a_1x^2 + a_0x^3$ is irreducible in $\mathbb{Q}[x]$, then $q(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ is also irreducible?

Published on 21 Mar 2024 - 4:43

score 55 · Answer 8 · 2026-03-27 18:19:23

55

Views

irreducibility in p-adic field

Published on 27 Mar 2026 - 18:19

score 51 · Answer 9 · 2024-03-23 15:48:01

51

Views

Missing and alternating coefficients of polynomials

Published on 23 Mar 2024 - 15:48

score 55 · Answer 10 · 2024-03-23 16:33:05

55

Views

A doubt about a given solution of the problem: Show that $x^2+1$ is irreducible over the integers mod $7.$

Published on 23 Mar 2024 - 16:33

score 48 · Answer 11 · 2024-03-24 00:28:24

48

Views

Prove that $f(x)$ is irreducible in $\mathbb{Z}$ with $f(b)$ a prime, $f(b-1) \neq 0$ and $\Re(\alpha_i) < b -1/2$

Published on 24 Mar 2024 - 0:28

score 64 · Answer 12 · 2024-03-25 12:00:48

64

Views

Prime ideals in $\mathbb{Z}[x]$ containing $\langle 3\rangle+\langle f\rangle$

Published on 25 Mar 2024 - 12:00

score 25 · Answer 13 · 2026-03-26 18:49:43

25

Views

Showing the polynomial has integer coefficients

Published on 26 Mar 2026 - 18:49

score 64 · Answer 14 · 2024-03-26 15:44:13

64

Views

Is a polynomial monotone when the first derivative has only imaginary roots?

Published on 26 Mar 2024 - 15:44

score 77 · Answer 15 · 2024-03-26 18:59:53

77

Views

Investigate whether the polynomial $q(x) = 2x^5 - 78x^3 + 39x + 21$ is irreducible in $\mathbb{F}_{13}[x]$.

Published on 26 Mar 2024 - 18:59

List Question

Equivalent definition of a perfect field

$L/K$ be a field extension with $Char(K) = p > 0$ and $[L : K] = n$ cannot be divided by $p$. Show that $L/K$ is separable.

Are two principal ideals are equal if their generator has the same root in some extension?

Irreducibility of the polynomial $x^n+5x+3$ over $\mathbb{Q}$

Fifth cyclotomic polynomial over a finite field

Decomposition of a polynomial of the form $X^{p^n}-X$ in finite fields.

If $p(x) = a_3 + a_2x + a_1x^2 + a_0x^3$ is irreducible in $\mathbb{Q}[x]$, then $q(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ is also irreducible?

irreducibility in p-adic field

Missing and alternating coefficients of polynomials

A doubt about a given solution of the problem: Show that $x^2+1$ is irreducible over the integers mod $7.$

Prove that $f(x)$ is irreducible in $\mathbb{Z}$ with $f(b)$ a prime, $f(b-1) \neq 0$ and $\Re(\alpha_i) < b -1/2$

Prime ideals in $\mathbb{Z}[x]$ containing $\langle 3\rangle+\langle f\rangle$

Showing the polynomial has integer coefficients

Is a polynomial monotone when the first derivative has only imaginary roots?

Investigate whether the polynomial $q(x) = 2x^5 - 78x^3 + 39x + 21$ is irreducible in $\mathbb{F}_{13}[x]$.

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