Question

Inverse of integral ideal in a Dedekind domain is a specific fractional ideal

score 43 · Answer 1 · 2023-07-17 20:30:41

43

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Inverse of integral ideal in a Dedekind domain is a specific fractional ideal

Published on 17 Jul 2023 - 20:30

score 51 · Answer 2 · 2023-07-18 11:49:39

51

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Question about Dedekind Domains and Valuations

Published on 18 Jul 2023 - 11:49

score 49 · Answer 3 · 2023-08-03 02:02:26

49

Views

Why is there a fractional ideal $\mathfrak b$ such that $\mathfrak a\mathfrak b=\mathfrak o$?

Published on 03 Aug 2023 - 2:02

score 52 · Answer 4 · 2023-08-13 22:38:48

52

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Equivalence of notions of localization for Dedekind domains

Published on 13 Aug 2023 - 22:38

score 34 · Answer 5 · 2023-08-20 10:59:22

34

Views

Show that $(p, \alpha)$ is a non-invertible ideal in the quadratic order $\mathcal{O}=\mathbb{Z}[\alpha]$

Published on 20 Aug 2023 - 10:59

score 39 · Answer 6 · 2023-08-24 09:56:26

39

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$M$ $\mathscr{R}$-submodule complete lattice $\iff$ $aL \subset M \subset a^{-1}L$, $a \in \mathscr{R}$

Published on 24 Aug 2023 - 9:56

score 44 · Answer 7 · 2023-08-30 13:21:25

44

Views

Prime of order is regular iff its decomposition in the normalization is trivial.

Published on 30 Aug 2023 - 13:21

score 28 · Answer 8 · 2026-03-16 18:22:32

28

Views

Tor-dimension of $A/(a)\otimes_k B$, where $A$ and $B$ are Dedekind domains

Published on 16 Mar 2026 - 18:22

score 53 · Answer 9 · 2023-10-02 03:47:56

53

Views

Dedekind domain, non PID, localization over maximal ideals.

Published on 02 Oct 2023 - 3:47

score 33 · Answer 10 · 2023-10-13 16:26:54

33

Views

Ad hoc proof of the fact that the localization of a ring of integers at a nonzero prime ideal is a PID

Published on 13 Oct 2023 - 16:26

score 56 · Answer 11 · 2023-11-16 19:56:33

56

Views

Is the integral closure of an integral domain a dedekind domain?

Published on 16 Nov 2023 - 19:56

score 89 · Answer 12 · 2023-11-20 22:00:17

89

Views

Can polynomial rings be classified as a specific type of ring like algebraic integers are classified as Dedekind domains??

Published on 20 Nov 2023 - 22:00

score 46 · Answer 13 · 2026-03-25 19:56:31

46

Views

Unique unramified ideal implies that the ramification index is equal to the degree of field extension in a galois extension

Published on 25 Mar 2026 - 19:56

score 122 · Answer 14 · 2024-02-04 19:50:18

122

Views

Counterexample of Divisibility of Ideals with Product of Ideals

Published on 04 Feb 2024 - 19:50

score 57 · Answer 15 · 2024-03-05 22:13:58

57

Views

Chinese Remainder Theorem and ideals generated in localizations

Published on 05 Mar 2024 - 22:13

List Question

Inverse of integral ideal in a Dedekind domain is a specific fractional ideal

Question about Dedekind Domains and Valuations

Why is there a fractional ideal $\mathfrak b$ such that $\mathfrak a\mathfrak b=\mathfrak o$?

Equivalence of notions of localization for Dedekind domains

Show that $(p, \alpha)$ is a non-invertible ideal in the quadratic order $\mathcal{O}=\mathbb{Z}[\alpha]$

$M$ $\mathscr{R}$-submodule complete lattice $\iff$ $aL \subset M \subset a^{-1}L$, $a \in \mathscr{R}$

Prime of order is regular iff its decomposition in the normalization is trivial.

Tor-dimension of $A/(a)\otimes_k B$, where $A$ and $B$ are Dedekind domains

Dedekind domain, non PID, localization over maximal ideals.

Ad hoc proof of the fact that the localization of a ring of integers at a nonzero prime ideal is a PID

Is the integral closure of an integral domain a dedekind domain?

Can polynomial rings be classified as a specific type of ring like algebraic integers are classified as Dedekind domains??

Unique unramified ideal implies that the ramification index is equal to the degree of field extension in a galois extension

Counterexample of Divisibility of Ideals with Product of Ideals

Chinese Remainder Theorem and ideals generated in localizations

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