Question

How can one split these kind of rings as a direct sum of minimal ideals

score 70 · Answer 1 · 2026-04-12 13:48:49

70

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How can one split these kind of rings as a direct sum of minimal ideals

Published on 12 Apr 2026 - 13:48

score 282 · Answer 2 · 2026-04-14 21:22:30

282

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Existence of an integral, primitive element $b\in L$, where $L\supset\text{Frac}(A)$, $A$ Dedekind

Published on 14 Apr 2026 - 21:22

score 509 · Answer 3 · 2026-04-11 07:01:32

509

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"Prime decomposition of $\infty$"

Published on 11 Apr 2026 - 7:01

score 1.7k · Answer 4 · 2026-04-12 00:03:18

1.7k

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What is Ring basis?

Published on 12 Apr 2026 - 0:03

score 81 · Answer 5 · 2026-04-15 23:38:33

81

Views

Finite extension of a field $\mathbb{F}_p$

Published on 15 Apr 2026 - 23:38

score 76 · Answer 6 · 2026-04-09 04:58:16

76

Views

Understanding the inductive proof about field extension in Artin

Published on 09 Apr 2026 - 4:58

score 1.5k · Answer 7 · 2026-04-16 07:07:41

1.5k

Views

Show that $Q[\sqrt3]$ is a field

Published on 16 Apr 2026 - 7:07

score 435 · Answer 8 · 2026-04-15 22:12:08

435

Views

Showing that $x^{14}+8x^{13}+3$ is irreducible in $ℚ[x]$ (need further explanation on the solution)

Published on 15 Apr 2026 - 22:12

score 52 · Answer 9 · 2026-04-11 18:09:00

52

Views

Finding minimum polynomial over the following field extentions

Published on 11 Apr 2026 - 18:09

score 246 · Answer 10 · 2026-04-17 11:13:25

Give an example of a cubic polynomial in $\mathbb{Q}[x]$ whose splitting field over $\mathbb{Q}$ has degree $8$ or explain why none exists

score 64 · Answer 11 · 2026-04-16 23:20:57

64

Views

Prove that no integer $w$ exists such that the splitting field of $x^4+x^3+x^2+x+1+w$ is that of $x^4+x^3+x^2+x+1$.

Published on 16 Apr 2026 - 23:20

score 337 · Answer 12 · 2026-04-13 23:49:19

337

Views

Show this field has no subfields but itself and the rationals

Published on 13 Apr 2026 - 23:49

score 60 · Answer 13 · 2026-04-12 07:03:46

60

Views

Representation of integer ring

Published on 12 Apr 2026 - 7:03

score 629 · Answer 14 · 2026-04-13 11:14:45

629

Views

Maximal real subfields of Cyclotomic subfields giving rise to identities

Published on 13 Apr 2026 - 11:14

score 85 · Answer 15 · 2026-04-16 22:53:27

85

Views

Show that if $a_1\alpha_1^m+a_2\alpha_2^m+\cdots+a_n\alpha_n^m =0$ for all $m \in \Bbb Z$, then $a_1 = \cdots = a_n = 0.$

Published on 16 Apr 2026 - 22:53

List Question

How can one split these kind of rings as a direct sum of minimal ideals

Existence of an integral, primitive element $b\in L$, where $L\supset\text{Frac}(A)$, $A$ Dedekind

"Prime decomposition of $\infty$"

What is Ring basis?

Finite extension of a field $\mathbb{F}_p$

Understanding the inductive proof about field extension in Artin

Show that $Q[\sqrt3]$ is a field

Showing that $x^{14}+8x^{13}+3$ is irreducible in $ℚ[x]$ (need further explanation on the solution)

Finding minimum polynomial over the following field extentions

Give an example of a cubic polynomial in $\mathbb{Q}[x]$ whose splitting field over $\mathbb{Q}$ has degree $8$ or explain why none exists

Prove that no integer $w$ exists such that the splitting field of $x^4+x^3+x^2+x+1+w$ is that of $x^4+x^3+x^2+x+1$.

Show this field has no subfields but itself and the rationals

Representation of integer ring

Maximal real subfields of Cyclotomic subfields giving rise to identities

Show that if $a_1\alpha_1^m+a_2\alpha_2^m+\cdots+a_n\alpha_n^m =0$ for all $m \in \Bbb Z$, then $a_1 = \cdots = a_n = 0.$

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