Question

Cancellation property holds in ideals in Dedekind domains

score 174 · Answer 1 · 2026-03-25 16:13:40

174

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Cancellation property holds in ideals in Dedekind domains

Published on 25 Mar 2026 - 16:13

score 69 · Answer 2 · 2026-04-15 15:19:13

69

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

Published on 15 Apr 2026 - 15:19

score 323 · Answer 3 · 2026-04-14 11:18:11

323

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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 14 Apr 2026 - 11:18

score 62 · Answer 4 · 2026-04-15 10:25:39

62

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

Published on 15 Apr 2026 - 10:25

score 87 · Answer 5 · 2026-04-16 16:16:44

87

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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 16 Apr 2026 - 16:16

score 625 · Answer 6 · 2026-04-16 08:28:20

625

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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 16 Apr 2026 - 8:28

score 73 · Answer 7 · 2026-04-10 19:24:30

73

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

Published on 10 Apr 2026 - 19:24

score 82 · Answer 8 · 2026-04-11 20:13:34

82

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powers of prime ideals in a Dedekind domain

Published on 11 Apr 2026 - 20:13

score 52 · Answer 9 · 2026-04-11 23:38:43

52

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

Published on 11 Apr 2026 - 23:38

score 693 · Answer 10 · 2026-04-12 17:52:00

693

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

Published on 12 Apr 2026 - 17:52

score 50 · Answer 11 · 2026-04-15 19:42:44

50

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

Published on 15 Apr 2026 - 19:42

score 194 · Answer 12 · 2026-04-13 23:51:52

194

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Non-maximal orders contains non-invertible ideals

Published on 13 Apr 2026 - 23:51

score 745 · Answer 13 · 2026-04-10 04:52:53

745

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

Published on 10 Apr 2026 - 4:52

score 67 · Answer 14 · 2026-04-12 02:28:31

67

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

Published on 12 Apr 2026 - 2:28

score 562 · Answer 15 · 2026-05-06 05:12:56

562

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Easy examples of integrally closed non-factorial domains?

Published on 06 May 2026 - 5:12

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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