Question

$A \cong D \subseteq B$ and $B/D \cong C$, is there any operation s.t $B$ can be "constructed" by combining $A$ and $C$ with that operation?

score 37 · Answer 1 · 2026-04-01 13:42:54

37

Views

$A \cong D \subseteq B$ and $B/D \cong C$, is there any operation s.t $B$ can be "constructed" by combining $A$ and $C$ with that operation?

Published on 01 Apr 2026 - 13:42

score 235 · Answer 2 · 2026-03-25 01:28:50

235

Views

Characterize the generators of the totally real subfield of an arbitrary cyclotomic field

Published on 25 Mar 2026 - 1:28

score 157 · Answer 3 · 2026-03-26 15:36:26

157

Views

Understanding Lang's Chapter 6 Theorem 9.1

Published on 26 Mar 2026 - 15:36

score 1k · Answer 4 · 2026-03-25 22:26:51

1k

Views

$f(x)$ is irreducible over finite field $F_p$ , does $f(x)$ split over $F_p / \langle f(x) \rangle$?

Published on 25 Mar 2026 - 22:26

score 48 · Answer 5 · 2026-03-30 18:06:06

48

Views

Proof that $F(a)=a+\langle f\rangle$ is an embedding from $K$ to $K[X]/\langle f\rangle$

Published on 30 Mar 2026 - 18:06

score 778 · Answer 6 · 2026-03-26 18:50:47

778

Views

Factor $X^4 + 3$ into irreducible factors in $F_7[X]$

Published on 26 Mar 2026 - 18:50

score 37 · Answer 7 · 2019-02-28 04:32:21

37

Views

Let $a \neq 0$ in a field $F$. Determine the integers $n \geq 1$ such that $x+a$ is a factor of $x^n+a^n$

Published on 28 Feb 2019 - 4:32

score 456 · Answer 8 · 2026-03-30 18:05:30

456

Views

$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$

Published on 30 Mar 2026 - 18:05

score 741 · Answer 9 · 2019-02-28 09:20:25

741

Views

How come algebraic closure is not unique?

Published on 28 Feb 2019 - 9:20

score 33 · Answer 10 · 2019-02-28 14:33:22

33

Views

Proposition 6.6. from Lang's Algebra

Published on 28 Feb 2019 - 14:33

score 61 · Answer 11 · 2026-03-26 18:51:48

61

Views

Questions about proof of existence of roots of $f$ in $K[X]/(f)$

Published on 26 Mar 2026 - 18:51

score 59 · Answer 12 · 2026-03-25 20:59:54

59

Views

Algebraic closure not even finitely generated over base field

Published on 25 Mar 2026 - 20:59

score 54 · Answer 13 · 2026-03-25 23:13:09

54

Views

Can $p(x)\in \mathbb{F}_{3}(x)$ with $p(x)=\frac{x²+x+1}{x+1}$ be expressed as a polynomial? Is it not possible for any of the given fields?

Published on 25 Mar 2026 - 23:13

score 81 · Answer 14 · 2019-03-02 20:25:50

81

Views

$x^2+ax+b=0 \overset ? \impliedby (A,+,\cdot)$ is a field

Published on 02 Mar 2019 - 20:25

score 66 · Answer 15 · 2026-03-28 10:55:44

66

Views

Example of certain polynomial over field

Published on 28 Mar 2026 - 10:55

List Question

$A \cong D \subseteq B$ and $B/D \cong C$, is there any operation s.t $B$ can be "constructed" by combining $A$ and $C$ with that operation?

Characterize the generators of the totally real subfield of an arbitrary cyclotomic field

Understanding Lang's Chapter 6 Theorem 9.1

$f(x)$ is irreducible over finite field $F_p$ , does $f(x)$ split over $F_p / \langle f(x) \rangle$?

Proof that $F(a)=a+\langle f\rangle$ is an embedding from $K$ to $K[X]/\langle f\rangle$

Factor $X^4 + 3$ into irreducible factors in $F_7[X]$

Let $a \neq 0$ in a field $F$. Determine the integers $n \geq 1$ such that $x+a$ is a factor of $x^n+a^n$

$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$

How come algebraic closure is not unique?

Proposition 6.6. from Lang's Algebra

Questions about proof of existence of roots of $f$ in $K[X]/(f)$

Algebraic closure not even finitely generated over base field

Can $p(x)\in \mathbb{F}_{3}(x)$ with $p(x)=\frac{x²+x+1}{x+1}$ be expressed as a polynomial? Is it not possible for any of the given fields?

$x^2+ax+b=0 \overset ? \impliedby (A,+,\cdot)$ is a field

Example of certain polynomial over field

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