Question

Extending "the ring of exponents" from $\Bbb{Z}$ to that which contains a solution to $4^x - 3 = 0 \pmod 5$?

score 66 · Answer 1 · 2026-02-23 06:05:41

66

Views

Extending "the ring of exponents" from $\Bbb{Z}$ to that which contains a solution to $4^x - 3 = 0 \pmod 5$?

Published on 23 Feb 2026 - 6:05

score 70 · Answer 2 · 2026-03-26 19:00:59

70

Views

Cubic extension adjoining a root of an irreducible cubic polynomial.

Published on 26 Mar 2026 - 19:00

score 31 · Answer 3 · 2020-03-11 17:30:47

31

Views

Field Extension example

Published on 11 Mar 2020 - 17:30

score 67 · Answer 4 · 2026-03-26 14:30:29

67

Views

Claim: $[K(\alpha_1, \dots \alpha_i): K] \leq n (n-1) \dots (n-i+1)$ for the splitting field of a separable polynomial of degree $n$

Published on 26 Mar 2026 - 14:30

score 156 · Answer 5 · 2020-03-14 12:38:33

156

Views

Which field extensions of $\mathbb Z$ are UFD?

Published on 14 Mar 2020 - 12:38

score 223 · Answer 6 · 2020-03-15 16:30:42

223

Views

$K$-homomorphisms for a field extension with a transcendental element

Published on 15 Mar 2020 - 16:30

score 168 · Answer 7 · 2020-03-15 21:39:30

168

Views

Extension of $\zeta_5^2 + \zeta_5^3$ over $ℚ$ is quadratic.

Published on 15 Mar 2020 - 21:39

score 211 · Answer 8 · 2026-04-01 20:22:21

211

Views

What is q-linear embedding?

Published on 01 Apr 2026 - 20:22

score 34 · Answer 9 · 2020-03-16 16:26:24

34

Views

When $\mathbb{C}(f,g)=\mathbb{C}(f',g')=\mathbb{C}(t)$.

Published on 16 Mar 2020 - 16:26

score 64 · Answer 10 · 2020-03-17 09:20:00

64

Views

$L \cong K(\sqrt{x}) \cong K[X]/(X^2-x)$ for $x \in K$

Published on 17 Mar 2020 - 9:20

score 65 · Answer 11 · 2020-03-17 22:15:47

65

Views

Are these fields equal?

Published on 17 Mar 2020 - 22:15

score 39 · Answer 12 · 2020-03-18 22:19:06

39

Views

Subset of separable elements of normal extension is normal

Published on 18 Mar 2020 - 22:19

score 96 · Answer 13 · 2020-03-19 13:06:59

96

Views

Prove that there is no intermediate field $K$ with $\mathbb{Q}\subset K\subsetneq \mathbb{C}$ with $\mathbb{C}/K$ purely transcendental.

Published on 19 Mar 2020 - 13:06

score 70 · Answer 14 · 2020-03-19 20:59:04

70

Views

Extension field exercise doubt

Published on 19 Mar 2020 - 20:59

score 56 · Answer 15 · 2026-03-26 14:31:59

56

Views

Show that $\frac{1+i}{\sqrt{2}}$ is in the splitting field of $x^8 - 3$ over $\mathbb{Q}$

Published on 26 Mar 2026 - 14:31

List Question

Extending "the ring of exponents" from $\Bbb{Z}$ to that which contains a solution to $4^x - 3 = 0 \pmod 5$?

Cubic extension adjoining a root of an irreducible cubic polynomial.

Field Extension example

Claim: $[K(\alpha_1, \dots \alpha_i): K] \leq n (n-1) \dots (n-i+1)$ for the splitting field of a separable polynomial of degree $n$

Which field extensions of $\mathbb Z$ are UFD?

$K$-homomorphisms for a field extension with a transcendental element

Extension of $\zeta_5^2 + \zeta_5^3$ over $ℚ$ is quadratic.

What is q-linear embedding?

When $\mathbb{C}(f,g)=\mathbb{C}(f',g')=\mathbb{C}(t)$.

$L \cong K(\sqrt{x}) \cong K[X]/(X^2-x)$ for $x \in K$

Are these fields equal?

Subset of separable elements of normal extension is normal

Prove that there is no intermediate field $K$ with $\mathbb{Q}\subset K\subsetneq \mathbb{C}$ with $\mathbb{C}/K$ purely transcendental.

Extension field exercise doubt

Show that $\frac{1+i}{\sqrt{2}}$ is in the splitting field of $x^8 - 3$ over $\mathbb{Q}$

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