List questions from dedekind-domain

Published on 19 Nov 2017 - 10:40

372

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Exercise $17$ $(e)$ on Marcus' Number Fields, Chapter $4$

Published on 20 Nov 2017 - 20:27

336

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Maximal ideals of $\mathbb Q[x,y]/(x^2+y^2+1)$

Published on 30 Nov 2017 - 4:02

478

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Exercise $23$ on Marcus's Number Fields, Chapter $4$

Published on 05 Dec 2017 - 17:37

266

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A reduction-step on a proof of Kronecker-Weber theorem

Published on 06 Dec 2017 - 1:14

159

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On a proof of Kronecker-Weber Theorem

Published on 06 Dec 2017 - 20:23

493

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There exists a unique abelian extension such that $[K:\mathbb{Q}]=p$ and $disc(K)=p^n$

Published on 08 Dec 2017 - 4:08

1.5k

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Every Ideal $\mathfrak{a}$ of a Dedekind domain $\mathcal{O}$ can be generated by $2$ elements

Published on 16 Dec 2017 - 2:52

481

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Localization of a Dedekind ring is a Dedekind ring or a field

Published on 18 Dec 2017 - 17:28

695

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Norm of an ideal with two generators in a ring of integers

Published on 20 Dec 2017 - 20:19

112

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Given a prime $\wp$, are there different primes $\wp_2$,..., $\wp_s$ such that $\wp \wp_2\cdots \wp_s$ is principal?

Published on 26 Mar 2026 - 17:33

225

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Dedekind domain and converse of Krull's principal ideal theorem

Published on 24 Dec 2017 - 20:46

56

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How to choose $a,b\in I$, so $ab\notin I^3$?

Published on 05 Jan 2018 - 19:33

1.9k

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A Noetherian ring with Krull dimension one which is not a Dedekind domain

Published on 03 Jan 2011 - 1:30

4.8k

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If $A$ is a Dedekind domain and $I \subset A$ a non-zero ideal, then every ideal of $A/I$ is principal.

Published on 14 Oct 2011 - 4:24

List Question

If the norm of an ideal is prime then the ideal is prime

Exercise $17$ $(e)$ on Marcus' Number Fields, Chapter $4$

Maximal ideals of $\mathbb Q[x,y]/(x^2+y^2+1)$

Exercise $23$ on Marcus's Number Fields, Chapter $4$

A reduction-step on a proof of Kronecker-Weber theorem

On a proof of Kronecker-Weber Theorem

There exists a unique abelian extension such that $[K:\mathbb{Q}]=p$ and $disc(K)=p^n$

Every Ideal $\mathfrak{a}$ of a Dedekind domain $\mathcal{O}$ can be generated by $2$ elements

Localization of a Dedekind ring is a Dedekind ring or a field

Norm of an ideal with two generators in a ring of integers

Given a prime $\wp$, are there different primes $\wp_2$,..., $\wp_s$ such that $\wp \wp_2\cdots \wp_s$ is principal?

Dedekind domain and converse of Krull's principal ideal theorem

How to choose $a,b\in I$, so $ab\notin I^3$?

A Noetherian ring with Krull dimension one which is not a Dedekind domain

If $A$ is a Dedekind domain and $I \subset A$ a non-zero ideal, then every ideal of $A/I$ is principal.

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