Question

Cancellation property holds in ideals in Dedekind domains

score 173 · Answer 1 · 2019-11-04 03:28:00

173

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Cancellation property holds in ideals in Dedekind domains

Published on 04 Nov 2019 - 3:28

score 66 · Answer 2 · 2019-11-04 04:14:46

66

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Let $K$ be an algebraic number field. Prove that $O_K$ contains infinitely many prime ideals.

Published on 04 Nov 2019 - 4:14

score 320 · Answer 3 · 2019-11-05 07:58:44

320

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Let $P$ be a prime ideal in the ring of integers then $P \cap \Bbb Z$ is prime in $\Bbb Z$

Published on 05 Nov 2019 - 7:58

score 60 · Answer 4 · 2019-11-05 08:51:35

60

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Prove that there exist only finitely many integral ideals of $O_K$ to which $m$ belongs

Published on 05 Nov 2019 - 8:51

score 84 · Answer 5 · 2019-11-05 23:01:52

84

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Prove that $P_1,\cdots,P_r$ are distinct prime ideals of $O_K$ with $<p>=P_1^{e_1}\cdots P_r^{e_r}$ and $N(P_i)=p^{deg f_i},i=1,2,\cdots,r$

Published on 05 Nov 2019 - 23:01

score 622 · Answer 6 · 2019-11-05 23:57:16

622

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Suppose that the prime $p$ is totally ramified in $O_{K_1}$ and unramified in $O_{K_2}$. Prove that $K_1 \cap K_2=\Bbb Q$.

Published on 05 Nov 2019 - 23:57

score 70 · Answer 7 · 2019-11-08 04:37:06

70

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Looking for an example of a non PIR commutative ring with every ideal two generated

Published on 08 Nov 2019 - 4:37

score 79 · Answer 8 · 2019-11-14 17:16:16

79

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powers of prime ideals in a Dedekind domain

Published on 14 Nov 2019 - 17:16

score 49 · Answer 9 · 2019-11-19 08:12:42

49

Views

Successive quotients of powers of a non-zero prime ideal in Dedekind domain

Published on 19 Nov 2019 - 8:12

score 690 · Answer 10 · 2019-11-24 11:49:10

690

Views

Is ring of $S$-integers a Dedekind domain?

Published on 24 Nov 2019 - 11:49

score 47 · Answer 11 · 2019-11-30 23:42:47

47

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Extension of $\mathbb{Q}$ by the positive $2^n$ roots of $3$

Published on 30 Nov 2019 - 23:42

score 191 · Answer 12 · 2019-12-01 23:46:27

191

Views

Non-maximal orders contains non-invertible ideals

Published on 01 Dec 2019 - 23:46

score 742 · Answer 13 · 2019-12-17 08:07:26

742

Views

Projective ideal in $\mathbb{Z}[\sqrt{-5}]$

Published on 17 Dec 2019 - 8:07

score 64 · Answer 14 · 2019-12-26 08:24:27

64

Views

$\operatorname{Spec}(A[\frac{b}{a}]) \longrightarrow \operatorname{Spec}(A)$ is an open immersion when $A$ is a Dedekind domain.

Published on 26 Dec 2019 - 8:24

score 560 · Answer 15 · 2026-02-23 06:01:54

560

Views

Easy examples of integrally closed non-factorial domains?

Published on 23 Feb 2026 - 6:01

List Question

Cancellation property holds in ideals in Dedekind domains

Let $K$ be an algebraic number field. Prove that $O_K$ contains infinitely many prime ideals.

Let $P$ be a prime ideal in the ring of integers then $P \cap \Bbb Z$ is prime in $\Bbb Z$

Prove that there exist only finitely many integral ideals of $O_K$ to which $m$ belongs

Prove that $P_1,\cdots,P_r$ are distinct prime ideals of $O_K$ with $<p>=P_1^{e_1}\cdots P_r^{e_r}$ and $N(P_i)=p^{deg f_i},i=1,2,\cdots,r$

Suppose that the prime $p$ is totally ramified in $O_{K_1}$ and unramified in $O_{K_2}$. Prove that $K_1 \cap K_2=\Bbb Q$.

Looking for an example of a non PIR commutative ring with every ideal two generated

powers of prime ideals in a Dedekind domain

Successive quotients of powers of a non-zero prime ideal in Dedekind domain

Is ring of $S$-integers a Dedekind domain?

Extension of $\mathbb{Q}$ by the positive $2^n$ roots of $3$

Non-maximal orders contains non-invertible ideals

Projective ideal in $\mathbb{Z}[\sqrt{-5}]$

$\operatorname{Spec}(A[\frac{b}{a}]) \longrightarrow \operatorname{Spec}(A)$ is an open immersion when $A$ is a Dedekind domain.

Easy examples of integrally closed non-factorial domains?

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