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Prime ideal in Dedekind domain

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Why do we want Dedekind rings to be integral closed?

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#abstract-algebra #commutative-algebra #dedekind-domain
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Properties of the first syzygy over Dedekind domains

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#commutative-algebra #ideals #dedekind-domain
182
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If $R$ is a Dedekind domain and $I, J \triangleleft R$, then $R^d \oplus I \simeq R^{d'} \oplus J$ implies $d = d'$ and $I \simeq J$

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#abstract-algebra #modules #projective-module #dedekind-domain
75
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On an auxiliary lemma for the structure theorem on Dedekind domains

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#modules #proof-explanation #dedekind-domain
547
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Rings over which every torsion-free module is projective

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76
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Integral ideals intersected with $\mathbb Z$

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61
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determine the set of prime ideals of the Dedekind Domain

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#abstract-algebra #commutative-algebra #ideals #dedekind-domain
168
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A Question from Neukirch Regarding the Quotient Module of a Sum of Modules

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#modules #algebraic-number-theory #dedekind-domain
91
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Ideal lying over an ideal shows up in prime decomposition

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#number-theory #algebraic-number-theory #maximal-and-prime-ideals #dedekind-domain
204
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about Dedekind domain

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#commutative-algebra #dedekind-domain
71
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What is the relation between torsion elements of the class group and covering spaces of curves?

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#abstract-algebra #algebraic-curves #covering-spaces #dedekind-domain #ideal-class-group
163
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Torsion module Finite composition length

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Showing that $x^2+5=y^3$ has no integer solutions.

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#number-theory #algebraic-number-theory #diophantine-equations #dedekind-domain
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Prove that the ring $\mathcal O_K$ of algebraic integers of $K = \Bbb Q (\sqrt d)$ is a Dedekind domain.

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