Question

Finding the irreducible polynomial from an element of a simple algebraic extension $K(\alpha)$

score 86 · Answer 1 · 2026-04-14 19:32:23

86

Views

Finding the irreducible polynomial from an element of a simple algebraic extension $K(\alpha)$

Published on 14 Apr 2026 - 19:32

score 142 · Answer 2 · 2026-04-16 01:38:51

142

Views

Given $K(\alpha)/K$ and $K(\beta)/K$ disjoint extensions with at least one of them odd degree then $K(\alpha,\beta)=K(\alpha\beta)$

Published on 16 Apr 2026 - 1:38

score 65 · Answer 3 · 2026-04-15 02:28:03

65

Views

In what fields does $\sum_{i=1}^nx_i^2=0$ imply that all the $x_i$'s are 0?

Published on 15 Apr 2026 - 2:28

score 112 · Answer 4 · 2026-04-19 03:56:56

112

Views

A generalization of a Puiseux field

Published on 19 Apr 2026 - 3:56

score 94 · Answer 5 · 2026-04-15 10:22:06

94

Views

Galois correspondence for $x^{5}-1$ of $x\rightarrow x^{4}$

Published on 15 Apr 2026 - 10:22

score 70 · Answer 6 · 2026-04-16 08:36:55

70

Views

Prove that $F=Z_3[x]/<x^2+x+2>$ is a splitting field for $f(x)=x^2+x+2$ over $Z_3$.

Published on 16 Apr 2026 - 8:36

score 635 · Answer 7 · 2026-04-17 13:09:17

635

Views

Verifying that the set {0,1} is a field

Published on 17 Apr 2026 - 13:09

score 193 · Answer 8 · 2026-04-10 10:27:28

193

Views

Degree of compositum of two abelian extensions

Published on 10 Apr 2026 - 10:27

score 26 · Answer 9 · 2026-04-17 05:25:06

26

Views

Does this iff statement apply to totally ordered sets?

Published on 17 Apr 2026 - 5:25

score 52 · Answer 10 · 2026-04-13 02:30:19

52

Views

Proving that the codomain of a bijective function is a field

Published on 13 Apr 2026 - 2:30

score 75 · Answer 11 · 2026-04-14 05:05:06

75

Views

Does there exist an irreducible factor of $x^{32}-x \in\mathbb{Z_3}[x]$ with degree 4?

Published on 14 Apr 2026 - 5:05

score 96 · Answer 12 · 2026-04-15 18:45:43

96

Views

Factoring an irreducible polynomial over $\mathbb{F}_q$ in $\mathbb{F}_{q^k}$

Published on 15 Apr 2026 - 18:45

score 479 · Answer 13 · 2026-04-14 21:48:14

479

Views

Suppose that $L:K$ is finite. Show that every K-monomorphism $L\to L$ is an automorphism. Does this result hold if the extension is not finite?

Published on 14 Apr 2026 - 21:48

score 620 · Answer 14 · 2026-04-15 11:35:11

620

Views

Prove R is a Field

Published on 15 Apr 2026 - 11:35

score 78 · Answer 15 · 2026-04-13 23:19:26

78

Views

Is it an element of $\mathbb{Q}[a]$?

Published on 13 Apr 2026 - 23:19

List Question

Finding the irreducible polynomial from an element of a simple algebraic extension $K(\alpha)$

Given $K(\alpha)/K$ and $K(\beta)/K$ disjoint extensions with at least one of them odd degree then $K(\alpha,\beta)=K(\alpha\beta)$

In what fields does $\sum_{i=1}^nx_i^2=0$ imply that all the $x_i$'s are 0?

A generalization of a Puiseux field

Galois correspondence for $x^{5}-1$ of $x\rightarrow x^{4}$

Prove that $F=Z_3[x]/<x^2+x+2>$ is a splitting field for $f(x)=x^2+x+2$ over $Z_3$.

Verifying that the set {0,1} is a field

Degree of compositum of two abelian extensions

Does this iff statement apply to totally ordered sets?

Proving that the codomain of a bijective function is a field

Does there exist an irreducible factor of $x^{32}-x \in\mathbb{Z_3}[x]$ with degree 4?

Factoring an irreducible polynomial over $\mathbb{F}_q$ in $\mathbb{F}_{q^k}$

Suppose that $L:K$ is finite. Show that every K-monomorphism $L\to L$ is an automorphism. Does this result hold if the extension is not finite?

Prove R is a Field

Is it an element of $\mathbb{Q}[a]$?

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