Question

Determine singular primes of quadratic ring $\mathbb{Z}[\sqrt{d}]$

score 225 · Answer 1 · 2018-10-13 13:42:27

225

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Determine singular primes of quadratic ring $\mathbb{Z}[\sqrt{d}]$

Published on 13 Oct 2018 - 13:42

score 56 · Answer 2 · 2026-03-28 10:04:34

56

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$B/\hat{B}$ is integral over $A / \hat{p}$ when $B$ is integral over $A$ and $\hat{B} \cap A = \hat{p}$.

Published on 28 Mar 2026 - 10:04

score 68 · Answer 3 · 2026-04-12 01:07:20

68

Views

Show determinant of matrix formed by trace of basis of ring of integer is independent of the basis chosen

Published on 12 Apr 2026 - 1:07

score 172 · Answer 4 · 2026-03-25 10:57:24

172

Views

Are there online Euclidean GCD calculators for Euclidean domains other than $\textbf Z$?

Published on 25 Mar 2026 - 10:57

score 799 · Answer 5 · 2026-04-10 05:05:39

799

Views

What is the worst case for the Euclidean algorithm in $\mathbb Z[i]$?

Published on 10 Apr 2026 - 5:05

score 59 · Answer 6 · 2026-04-13 12:30:42

59

Views

Lower bound on the value of a polynomial

Published on 13 Apr 2026 - 12:30

score 123 · Answer 7 · 2026-04-13 04:53:36

123

Views

How to show the set $\operatorname{Hom}_K(L,\bar{K})$ of all $K$-embeddings of $L$ is partitioned into $m$ equivalence classes of $d$ elements each?

Published on 13 Apr 2026 - 4:53

score 114 · Answer 8 · 2026-04-11 19:38:57

114

Views

Local-global property for Diophantine equations over $\mathbb{Z}$

Published on 11 Apr 2026 - 19:38

score 133 · Answer 9 · 2026-03-25 04:41:31

133

Views

Given $a, b$ coprime integers, show that any factor of $a^2 - 2b^2$ is of the form $c^2 - 2d^2$

Published on 25 Mar 2026 - 4:41

score 537 · Answer 10 · 2026-04-12 23:55:27

537

Views

What is the order of an unramified character?

Published on 12 Apr 2026 - 23:55

score 195 · Answer 11 · 2018-10-17 05:06:16

195

Views

Ideal class group of $K = \mathbb{Q}[x]/ (x^{3} + 11x + 21)$

Published on 17 Oct 2018 - 5:06

score 87 · Answer 12 · 2026-04-12 21:46:20

87

Views

Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

Published on 12 Apr 2026 - 21:46

score 678 · Answer 13 · 2026-04-11 07:26:49

678

Views

Is $\pi/e$ a period?

Published on 11 Apr 2026 - 7:26

score 36 · Answer 14 · 2026-04-13 07:43:29

36

Views

Non-archimedean valuation and squares

Published on 13 Apr 2026 - 7:43

score 275 · Answer 15 · 2026-04-13 11:08:47

275

Views

Why are all Frobenius elements conjugated?

Published on 13 Apr 2026 - 11:08

List Question

Determine singular primes of quadratic ring $\mathbb{Z}[\sqrt{d}]$

$B/\hat{B}$ is integral over $A / \hat{p}$ when $B$ is integral over $A$ and $\hat{B} \cap A = \hat{p}$.

Show determinant of matrix formed by trace of basis of ring of integer is independent of the basis chosen

Are there online Euclidean GCD calculators for Euclidean domains other than $\textbf Z$?

What is the worst case for the Euclidean algorithm in $\mathbb Z[i]$?

Lower bound on the value of a polynomial

How to show the set $\operatorname{Hom}_K(L,\bar{K})$ of all $K$-embeddings of $L$ is partitioned into $m$ equivalence classes of $d$ elements each?

Local-global property for Diophantine equations over $\mathbb{Z}$

Given $a, b$ coprime integers, show that any factor of $a^2 - 2b^2$ is of the form $c^2 - 2d^2$

What is the order of an unramified character?

Ideal class group of $K = \mathbb{Q}[x]/ (x^{3} + 11x + 21)$

Should the terminology "$K$-embedding" be regarded as a homomorphism of $K$ -vector spaces?

Is $\pi/e$ a period?

Non-archimedean valuation and squares

Why are all Frobenius elements conjugated?

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