Question

Fixed field and prime field

score 118 · Answer 1 · 2026-03-29 15:31:21

118

Views

Fixed field and prime field

Published on 29 Mar 2026 - 15:31

score 182 · Answer 2 · 2026-03-26 00:53:50

182

Views

Factoring $x^8-1$ into a product of irreducibles over $\mathbb{Z}$ and $\mathbb{Z_2}$

Published on 26 Mar 2026 - 0:53

score 930 · Answer 3 · 2018-09-24 22:35:20

930

Views

A finite field with $p^s$ elements has only $s$ automorphisms.

Published on 24 Sep 2018 - 22:35

score 921 · Answer 4 · 2026-03-25 23:19:14

921

Views

Algebraic extensions are isomorphic if the same polynomials have roots

Published on 25 Mar 2026 - 23:19

score 105 · Answer 5 · 2026-03-29 13:27:20

105

Views

Separability of irreducible polynomial of degree 2

Published on 29 Mar 2026 - 13:27

score 560 · Answer 6 · 2026-02-23 01:23:46

560

Views

What is an example of a non-simple finite extension $K/F$ such that the purely inseparable closure of $F$ in $K$ is simple?

Published on 23 Feb 2026 - 1:23

score 74 · Answer 7 · 2026-03-29 13:24:20

74

Views

Is $Q( (1 + \frac{1}{2})^{2}, (1 + \frac{1}{3})^{3}, (1 + \frac{1}{4})^4, \ldots )$ an algebraic extension of $Q$?

Published on 29 Mar 2026 - 13:24

score 114 · Answer 8 · 2026-04-01 08:03:52

114

Views

Fields with Differential identity, and Amitsur-like results

Published on 01 Apr 2026 - 8:03

score 569 · Answer 9 · 2026-03-26 16:10:08

569

Views

Showing $Tr_{L/K} \circ Tr_{M/L} = Tr_{M/K}$ where $K \subseteq L \subseteq M$ is a tower of field extensions - Algebraic Number Theory by Neukerich

Published on 26 Mar 2026 - 16:10

score 153 · Answer 10 · 2026-03-29 13:27:44

153

Views

Does $K[\alpha]$ has an inverse of $\alpha$ if this element is algebraic?

Published on 29 Mar 2026 - 13:27

score 353 · Answer 11 · 2026-04-01 12:47:16

353

Views

If $E$ is algebraic extension field of $F$, then also $E(x)$ is algebraic extension of $F(x)$?

Published on 01 Apr 2026 - 12:47

score 44 · Answer 12 · 2026-03-25 16:13:53

44

Views

Can two splitting fields over the same field of a polynomial be different (in the set sense and not up to isomorphism)?

Published on 25 Mar 2026 - 16:13

score 76 · Answer 13 · 2018-09-28 14:12:16

76

Views

Algebra's exercise about algebraic extension of fields

Published on 28 Sep 2018 - 14:12

score 1.2k · Answer 14 · 2026-03-27 03:44:07

1.2k

Views

Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$.

Published on 27 Mar 2026 - 3:44

score 65 · Answer 15 · 2026-03-25 19:06:39

65

Views

$n$ for which no polynomial of degree $n$ is irreducible in $\mathbb{Z}_n[X]$

Published on 25 Mar 2026 - 19:06

List Question

Fixed field and prime field

Factoring $x^8-1$ into a product of irreducibles over $\mathbb{Z}$ and $\mathbb{Z_2}$

A finite field with $p^s$ elements has only $s$ automorphisms.

Algebraic extensions are isomorphic if the same polynomials have roots

Separability of irreducible polynomial of degree 2

What is an example of a non-simple finite extension $K/F$ such that the purely inseparable closure of $F$ in $K$ is simple?

Is $Q( (1 + \frac{1}{2})^{2}, (1 + \frac{1}{3})^{3}, (1 + \frac{1}{4})^4, \ldots )$ an algebraic extension of $Q$?

Fields with Differential identity, and Amitsur-like results

Showing $Tr_{L/K} \circ Tr_{M/L} = Tr_{M/K}$ where $K \subseteq L \subseteq M$ is a tower of field extensions - Algebraic Number Theory by Neukerich

Does $K[\alpha]$ has an inverse of $\alpha$ if this element is algebraic?

If $E$ is algebraic extension field of $F$, then also $E(x)$ is algebraic extension of $F(x)$?

Can two splitting fields over the same field of a polynomial be different (in the set sense and not up to isomorphism)?

Algebra's exercise about algebraic extension of fields

Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$.

$n$ for which no polynomial of degree $n$ is irreducible in $\mathbb{Z}_n[X]$

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