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Application Chinese Remainder Theorem to Dedekind Domains

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#commutative-algebra #dedekind-domain
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How does passing to ideals solve the problem of unique factorization?

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#number-theory #algebraic-number-theory #dedekind-domain
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Proof that ideals of Dedekind domains are generated by at most two elements: how does the bolded step in the proof work?

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#commutative-algebra #dedekind-domain
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Show that a ring is a Dedekind domain

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#commutative-algebra #maximal-and-prime-ideals #dedekind-domain
65
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Is $M_n(R)$ Dedekind if $R$ is Dedekind?

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#abstract-algebra #matrices #ring-theory #dedekind-domain
115
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Prime decomposition in a Dedekind domain

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#commutative-algebra #modules #finitely-generated #dedekind-domain
33
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Every cut in R+ ist a dedekind cut?

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#complex-analysis #dedekind-domain
957
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Ideal Class Group of $\mathbb{Q}(\sqrt{65})$

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#abstract-algebra #algebraic-number-theory #extension-field #dedekind-domain
714
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There exist an integral ideal prime to a given nonzero integral ideal

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#algebraic-number-theory #dedekind-domain
441
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Characteristic of residue field in a Dedekind domain.

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#abstract-algebra #number-theory #dedekind-domain #ramification #positive-characteristic
192
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Serre's (Krull's) criterion for normality in practice

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#algebraic-geometry #commutative-algebra #dedekind-domain
140
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Fractional ideals problem

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#abstract-algebra #dedekind-domain
186
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Ideals in quotients of Dedekind domains

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#abstract-algebra #dedekind-domain
192
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Fractional ideals are isomorphic to relatively prime integral ideals in Dedekind domains

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#abstract-algebra #dedekind-domain
641
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Is a number ring a Dedekind domain?

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#number-theory #algebraic-number-theory #dedekind-domain

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