Question

A curious condition for $f$ being irreducible in $\mathbb{Q}$[x]

score 281 · Answer 1 · 2026-03-27 15:07:22

281

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A curious condition for $f$ being irreducible in $\mathbb{Q}$[x]

Published on 27 Mar 2026 - 15:07

score 68 · Answer 2 · 2026-04-01 09:55:33

68

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$α$ root of $f$, $β$ root of $g$. Show $f$ irred. in $\mathbb{Q}(β)$ iff $g$ irred. in $\mathbb{Q}(α)$

Published on 01 Apr 2026 - 9:55

score 85 · Answer 3 · 2019-09-27 06:40:48

85

Views

characterization of number fields that occur inside some prime cyclotomic field?

Published on 27 Sep 2019 - 6:40

score 126 · Answer 4 · 2026-03-26 23:10:45

126

Views

Proof check that the composite of $\sigma K$ is precisely the galois closure $L$ of $K/F$.

Published on 26 Mar 2026 - 23:10

score 780 · Answer 5 · 2026-03-27 13:47:31

780

Views

Stabilizer (orbit) of polynomials and Galois group and correspondence

Published on 27 Mar 2026 - 13:47

score 447 · Answer 6 · 2019-09-29 16:05:06

447

Views

Restriction map of Galois groups

Published on 29 Sep 2019 - 16:05

score 130 · Answer 7 · 2026-03-27 15:05:37

130

Views

If $p$ prime, $a∈\mathbb{Z}$ , $n∈\mathbb{N}$, $g∈\mathbb{Z} [x]$, deg $g < n$, $p \nmid g(a)$ then $(x − a)^n + p · g(x)$ irred. $\mathbb{Q}[x]$

Published on 27 Mar 2026 - 15:05

score 44 · Answer 8 · 2019-09-30 17:11:19

44

Views

Why does $\chi (L,L) \subseteq \text{End}_{K} (L)$?

Published on 30 Sep 2019 - 17:11

score 324 · Answer 9 · 2026-04-01 10:02:33

324

Views

Does cyclic field imply Galois?

Published on 01 Apr 2026 - 10:02

score 514 · Answer 10 · 2026-03-26 12:34:38

514

Views

Elementary Symmetric Polynomials, Roots of cubic polynomials

Published on 26 Mar 2026 - 12:34

score 163 · Answer 11 · 2026-03-26 09:44:47

163

Views

Unique "splitting fields" for infinite polynomials

Published on 26 Mar 2026 - 9:44

score 1.7k · Answer 12 · 2026-04-01 09:54:45

1.7k

Views

Degree of extensions and their composite

Published on 01 Apr 2026 - 9:54

score 623 · Answer 13 · 2026-04-01 03:10:45

623

Views

Density of set of splitting primes

Published on 01 Apr 2026 - 3:10

score 60 · Answer 14 · 2014-03-12 20:50:21

60

Views

Degree 3 polynomial with coef in a field K: question on roots in a algebraic closure

Published on 12 Mar 2014 - 20:50

score 982 · Answer 15 · 2014-03-13 00:40:37

982

Views

If $\alpha$ is an algebraic number, then prove that $\frac{2}{3}\alpha$ is also algebraic.

Published on 13 Mar 2014 - 0:40

List Question

A curious condition for $f$ being irreducible in $\mathbb{Q}$[x]

$α$ root of $f$, $β$ root of $g$. Show $f$ irred. in $\mathbb{Q}(β)$ iff $g$ irred. in $\mathbb{Q}(α)$

characterization of number fields that occur inside some prime cyclotomic field?

Proof check that the composite of $\sigma K$ is precisely the galois closure $L$ of $K/F$.

Stabilizer (orbit) of polynomials and Galois group and correspondence

Restriction map of Galois groups

If $p$ prime, $a∈\mathbb{Z}$ , $n∈\mathbb{N}$, $g∈\mathbb{Z} [x]$, deg $g < n$, $p \nmid g(a)$ then $(x − a)^n + p · g(x)$ irred. $\mathbb{Q}[x]$

Why does $\chi (L,L) \subseteq \text{End}_{K} (L)$?

Does cyclic field imply Galois?

Elementary Symmetric Polynomials, Roots of cubic polynomials

Unique "splitting fields" for infinite polynomials

Degree of extensions and their composite

Density of set of splitting primes

Degree 3 polynomial with coef in a field K: question on roots in a algebraic closure

If $\alpha$ is an algebraic number, then prove that $\frac{2}{3}\alpha$ is also algebraic.

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