Question

Separability of irreducible polynomial of degree 2

score 104 · Answer 1 · 2018-09-26 06:33:40

104

Views

Separability of irreducible polynomial of degree 2

Published on 26 Sep 2018 - 6:33

score 560 · Answer 2 · 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 73 · Answer 3 · 2018-09-26 16:08:39

73

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 26 Sep 2018 - 16:08

score 569 · Answer 4 · 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 152 · Answer 5 · 2018-09-27 15:58:26

152

Views

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

Published on 27 Sep 2018 - 15:58

score 352 · Answer 6 · 2026-03-20 03:47:23

352

Views

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

Published on 20 Mar 2026 - 3:47

score 47 · Answer 7 · 2018-10-01 23:11:22

47

Views

$\sqrt{a-b\sqrt{c}} \in \mathbb Q(\sqrt{a+b\sqrt{c}})$

Published on 01 Oct 2018 - 23:11

score 31 · Answer 8 · 2018-10-02 14:27:55

31

Views

An algebraic extension of degree 3

Published on 02 Oct 2018 - 14:27

score 50 · Answer 9 · 2018-10-02 19:58:33

50

Views

Find a field $F$ such that $[F : \mathbb{Q}] = 3$ and $F \ne \mathbb{Q }(\sqrt[3]{a}), \forall a \in \mathbb{Q}$

Published on 02 Oct 2018 - 19:58

score 114 · Answer 10 · 2026-03-25 16:14:00

114

Views

degree of splitting field of p(q(x))

Published on 25 Mar 2026 - 16:14

score 104 · Answer 11 · 2026-03-25 16:14:04

104

Views

degree of splitting field of palindromic polynomial

Published on 25 Mar 2026 - 16:14

score 293 · Answer 12 · 2018-10-03 21:06:37

293

Views

Dimensions with Fields and Subfields

Published on 03 Oct 2018 - 21:06

score 446 · Answer 13 · 2026-03-24 22:01:44

446

Views

$\mathbb Q(\zeta_m)\cap\mathbb Q(\zeta_n)=\mathbb Q(\zeta_d)$

Published on 24 Mar 2026 - 22:01

score 56 · Answer 14 · 2018-10-07 11:53:46

56

Views

Why $\mathcal O_L/\mathfrak P_i$ is a finite extension of $\mathcal O_K/\mathfrak p$?

Published on 07 Oct 2018 - 11:53

score 52 · Answer 15 · 2018-10-07 23:28:42

52

Views

Let $E/\ F$ be a fine extension of fields that $E = F[\alpha]$, show that if the minimal polynomial $f (x)$ of $\alpha$...

Published on 07 Oct 2018 - 23:28

List Question

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 $Q$?

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 $F(x)$?

$\sqrt{a-b\sqrt{c}} \in \mathbb Q(\sqrt{a+b\sqrt{c}})$

An algebraic extension of degree 3

Find a field $F$ such that $[F : \mathbb{Q}] = 3$ and $F \ne \mathbb{Q }(\sqrt[3]{a}), \forall a \in \mathbb{Q}$

degree of splitting field of p(q(x))

degree of splitting field of palindromic polynomial

Dimensions with Fields and Subfields

$\mathbb Q(\zeta_m)\cap\mathbb Q(\zeta_n)=\mathbb Q(\zeta_d)$

Why $\mathcal O_L/\mathfrak P_i$ is a finite extension of $\mathcal O_K/\mathfrak p$?

Let $E/\ F$ be a fine extension of fields that $E = F[\alpha]$, show that if the minimal polynomial $f (x)$ of $\alpha$...

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