Question

Compute $d(n) = [\mathbb{F}_3[a] : \mathbb{F}_3]$ where $a\in K^\times$ has order $n$ and $K$ is a field with $81$ elements.

score 69 · Answer 1 · 2026-04-16 14:44:25

69

Views

Compute $d(n) = [\mathbb{F}_3[a] : \mathbb{F}_3]$ where $a\in K^\times$ has order $n$ and $K$ is a field with $81$ elements.

Published on 16 Apr 2026 - 14:44

score 91 · Answer 2 · 2026-05-15 13:14:40

91

Views

$\Bbb Q \subseteq \Bbb Q(\sqrt {a + \sqrt b})$ is normal iff at least one of $a^2 − b$ and $(a^2 − b)/b$ is a square in $ \Bbb Q$

Published on 15 May 2026 - 13:14

score 43 · Answer 3 · 2026-04-15 15:05:29

43

Views

Irreducibility of polynomial in the ring $R[X, Y]$ where $R$ is a field

Published on 15 Apr 2026 - 15:05

score 110 · Answer 4 · 2026-04-15 22:59:38

110

Views

Why isn't $\mathbb{Q}(i \sqrt{2})$ a splitting field for $x^{2}+2$ over $\mathbb{Q}$?

Published on 15 Apr 2026 - 22:59

score 139 · Answer 5 · 2026-04-16 18:34:25

139

Views

$L/K$ being formally smooth implies $L/K$ is separable?

Published on 16 Apr 2026 - 18:34

score 37 · Answer 6 · 2026-04-09 16:54:47

37

Views

Definition of simple radical extension.

Published on 09 Apr 2026 - 16:54

score 122 · Answer 7 · 2026-04-29 22:02:11

122

Views

Subquotients after extension of scalars

Published on 29 Apr 2026 - 22:02

score 23 · Answer 8 · 2026-05-02 08:52:08

23

Views

Multiplicativity of the degree of separability

Published on 02 May 2026 - 8:52

score 85 · Answer 9 · 2026-04-16 03:51:16

85

Views

Proving $\mathbb{Q}_{p}$ is unique up to unique isomorphism

Published on 16 Apr 2026 - 3:51

score 51 · Answer 10 · 2026-04-29 22:02:33

51

Views

Let $M_i$ be the free $\mathbb Z$ module $\mathbb Z,$ and let $M$ be the direct product

Published on 29 Apr 2026 - 22:02

score 23 · Answer 11 · 2026-04-25 01:28:51

23

Views

Are the invertible matrices which are used to find the SNF always part of the ideal principle domain?

Published on 25 Apr 2026 - 1:28

score 73 · Answer 12 · 2026-05-15 13:07:55

73

Views

Extending a field homomorphism on a finite field

Published on 15 May 2026 - 13:07

score 95 · Answer 13 · 2026-04-16 07:25:39

95

Views

Find a normal basis for $\Bbb F_2[\omega]$ over $\Bbb F_2$.

Published on 16 Apr 2026 - 7:25

score 46 · Answer 14 · 2026-04-09 04:43:47

46

Views

Extending homomorphism from from splitting field of a polynomial to another field where that polynomial splits into linear factor

Published on 09 Apr 2026 - 4:43

score 65 · Answer 15 · 2026-04-12 23:08:24

65

Views

Maximal ideals of $F[x]/(x^2)$

Published on 12 Apr 2026 - 23:08

List Question

Compute $d(n) = [\mathbb{F}_3[a] : \mathbb{F}_3]$ where $a\in K^\times$ has order $n$ and $K$ is a field with $81$ elements.

$\Bbb Q \subseteq \Bbb Q(\sqrt {a + \sqrt b})$ is normal iff at least one of $a^2 − b$ and $(a^2 − b)/b$ is a square in $ \Bbb Q$

Irreducibility of polynomial in the ring $R[X, Y]$ where $R$ is a field

Why isn't $\mathbb{Q}(i \sqrt{2})$ a splitting field for $x^{2}+2$ over $\mathbb{Q}$?

$L/K$ being formally smooth implies $L/K$ is separable?

Definition of simple radical extension.

Subquotients after extension of scalars

Multiplicativity of the degree of separability

Proving $\mathbb{Q}_{p}$ is unique up to unique isomorphism

Let $M_i$ be the free $\mathbb Z$ module $\mathbb Z,$ and let $M$ be the direct product

Are the invertible matrices which are used to find the SNF always part of the ideal principle domain?

Extending a field homomorphism on a finite field

Find a normal basis for $\Bbb F_2[\omega]$ over $\Bbb F_2$.

Extending homomorphism from from splitting field of a polynomial to another field where that polynomial splits into linear factor

Maximal ideals of $F[x]/(x^2)$

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