Question

If $R$ is a UFD, find $I$ such that $R[\alpha]\cong R[X]/I$

score 114 · Answer 1 · 2026-04-11 19:10:02

114

Views

If $R$ is a UFD, find $I$ such that $R[\alpha]\cong R[X]/I$

Published on 11 Apr 2026 - 19:10

score 23 · Answer 2 · 2026-04-13 22:33:27

23

Views

$[K:k]_i<\infty$. Show that $kK^{p^n} = kK^{p^e}$ for all $n\ge e.$

Published on 13 Apr 2026 - 22:33

score 114 · Answer 3 · 2026-04-15 14:41:53

114

Views

Are elements of $\mathbb{Q}$ unique by value?

Published on 15 Apr 2026 - 14:41

score 85 · Answer 4 · 2026-04-14 10:48:53

85

Views

Prove an equation is solvable/unsolvable

Published on 14 Apr 2026 - 10:48

score 322 · Answer 5 · 2026-04-16 22:44:42

322

Views

Prove that the field $\mathbb{F}_{p}$ is not algebraically closed where $p$ is prime

Published on 16 Apr 2026 - 22:44

score 1.8k · Answer 6 · 2026-04-14 19:46:14

1.8k

Views

Let $_{125}$ be the field of $125$ elements. The number of non-zero elements $ ∈ _{125}$ such that $^5 =\alpha$?

Published on 14 Apr 2026 - 19:46

score 202 · Answer 7 · 2026-04-14 17:51:03

202

Views

Relationship between $x^{p-1} - a$ and $x^p - ax - b$

Published on 14 Apr 2026 - 17:51

score 356 · Answer 8 · 2026-04-13 06:02:06

356

Views

The set of algebraic numbers is countable

Published on 13 Apr 2026 - 6:02

score 147 · Answer 9 · 2026-03-26 17:53:30

147

Views

What is the known form of this transcendental number theorem suggesting $e\times\pi$ is very unlikely to be algebraic?

Published on 26 Mar 2026 - 17:53

score 1.5k · Answer 10 · 2026-04-17 09:43:26

1.5k

Views

Degree of $\mathbb{Q}(\zeta_n)$ over $\mathbb{Q}(\zeta_n+\zeta_{n}^{-1})$

Published on 17 Apr 2026 - 9:43

score 122 · Answer 11 · 2026-04-13 23:15:33

122

Views

Prove $\mathbb{R}$ does not contain a subring isomorphic to $\mathbb{C}$

Published on 13 Apr 2026 - 23:15

score 825 · Answer 12 · 2026-04-11 23:38:03

825

Views

Subfields of $\mathbb{C}$ isomorphic to $\mathbb{R}$

Published on 11 Apr 2026 - 23:38

score 100 · Answer 13 · 2026-04-22 09:45:38

100

Views

Symbol for quotient field of an integral domain

Published on 22 Apr 2026 - 9:45

score 206 · Answer 14 · 2026-04-16 19:11:21

206

Views

Showing $\mathbf Q(\sqrt2,\sqrt3)=\mathbf Q(\sqrt2+\sqrt3)$

Published on 16 Apr 2026 - 19:11

score 397 · Answer 15 · 2026-04-12 21:52:32

397

Views

Derivations and algebraic extensions in characteristic zero

Published on 12 Apr 2026 - 21:52

List Question

If $R$ is a UFD, find $I$ such that $R[\alpha]\cong R[X]/I$

$[K:k]_i<\infty$. Show that $kK^{p^n} = kK^{p^e}$ for all $n\ge e.$

Are elements of $\mathbb{Q}$ unique by value?

Prove an equation is solvable/unsolvable

Prove that the field $\mathbb{F}_{p}$ is not algebraically closed where $p$ is prime

Let $_{125}$ be the field of $125$ elements. The number of non-zero elements $ ∈ _{125}$ such that $^5 =\alpha$?

Relationship between $x^{p-1} - a$ and $x^p - ax - b$

The set of algebraic numbers is countable

What is the known form of this transcendental number theorem suggesting $e\times\pi$ is very unlikely to be algebraic?

Degree of $\mathbb{Q}(\zeta_n)$ over $\mathbb{Q}(\zeta_n+\zeta_{n}^{-1})$

Prove $\mathbb{R}$ does not contain a subring isomorphic to $\mathbb{C}$

Subfields of $\mathbb{C}$ isomorphic to $\mathbb{R}$

Symbol for quotient field of an integral domain

Showing $\mathbf Q(\sqrt2,\sqrt3)=\mathbf Q(\sqrt2+\sqrt3)$

Derivations and algebraic extensions in characteristic zero

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