List questions from algebraic-number-theory

Published on 25 Mar 2026 - 19:06

479

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Primitive binary quadratic forms.

Published on 25 Mar 2026 - 2:56

190

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Proving $5S= \langle 5,{\alpha} +2\rangle\,\langle 5, {\alpha}^2+3{\alpha}-1\rangle$

Published on 25 Mar 2026 - 17:43

324

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Cyclotomic Fields are equal?

Published on 05 Apr 2026 - 16:37

72

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If $ \mathrm{disc}(\alpha_1,\alpha_2,\cdots,\alpha_n)$ is square-free, then $\{ \alpha_1, \alpha_2, \cdots, \alpha_n\}$ is an integral basis

Published on 12 Jul 2018 - 17:54

77

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fractional ideal $I$ in number field and codifferent $C$ are related by $\operatorname{Hom}(I, \mathbb{Z}) \cong I^{-1} \otimes C $

Published on 12 Jul 2018 - 19:49

572

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Totally real subfields

Published on 04 Apr 2026 - 13:27

154

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Example of the set of absolute value on number fields.

Published on 25 Mar 2026 - 9:53

295

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$\mathbb{Z}_{(p)}[\zeta]$ principal ideal domain

Published on 11 Apr 2026 - 12:08

278

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$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$

Published on 12 Apr 2026 - 6:59

49

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Inference of a condition

Published on 12 Apr 2026 - 3:14

418

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Zagiers Class Number Definition of Binary Quadratic Forms

Published on 11 Apr 2026 - 22:39

85

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On the equivalence of ideals coming from equivalence binary quadratic forms

Published on 24 Mar 2026 - 19:09

398

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Proof that the algebraic integers form a subring of $\mathbb{C}$

Published on 26 Mar 2026 - 10:59

193

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(Real) Algebraic numbers that aren't constructible or roots

Published on 09 Apr 2026 - 4:31

List Question

The conductor of the Hilbert class field of a number field

Primitive binary quadratic forms.

Proving $5S= \langle 5,{\alpha} +2\rangle\,\langle 5, {\alpha}^2+3{\alpha}-1\rangle$

Cyclotomic Fields are equal?

If $ \mathrm{disc}(\alpha_1,\alpha_2,\cdots,\alpha_n)$ is square-free, then $\{ \alpha_1, \alpha_2, \cdots, \alpha_n\}$ is an integral basis

fractional ideal $I$ in number field and codifferent $C$ are related by $\operatorname{Hom}(I, \mathbb{Z}) \cong I^{-1} \otimes C $

Totally real subfields

Example of the set of absolute value on number fields.

$\mathbb{Z}_{(p)}[\zeta]$ principal ideal domain

$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$

Inference of a condition

Zagiers Class Number Definition of Binary Quadratic Forms

On the equivalence of ideals coming from equivalence binary quadratic forms

Proof that the algebraic integers form a subring of $\mathbb{C}$

(Real) Algebraic numbers that aren't constructible or roots

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