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Elements of a Dedekind domain can be chosen to have valuation $1$ with respect to one prime, $0$ everywhere else

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#abstract-algebra #number-theory #dedekind-domain
146
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Degree of extension is equal to linear combination of prime factor multiplicities with prime factor index coefficients in Dedekind domains

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#commutative-algebra #algebraic-number-theory #ideals #dedekind-domain
369
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Projectiveness and Dedekind domains

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#ring-theory #commutative-algebra #modules #dedekind-domain
370
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Free abelian group of fractional ideals

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#abstract-algebra #group-theory #algebraic-number-theory #free-groups #dedekind-domain
265
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Product of two ideals in Dedekind domains

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#abstract-algebra #ideals #dedekind-domain
860
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Dedekind's criterion clarification

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#algebraic-number-theory #ideals #dedekind-domain
127
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Ideal in Dedekind domain

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#algebraic-number-theory #ideals #noetherian #dedekind-domain
104
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To show a certain integral closure is an order.

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#abstract-algebra #ring-theory #commutative-algebra #dedekind-domain
341
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Valuation associated to a non-zero prime ideal of the ring of integers

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#number-theory #ring-theory #algebraic-number-theory #dedekind-domain
184
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Localization of lattices over Dedekind domains

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#abstract-algebra #algebraic-number-theory #dedekind-domain
1k
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Localization of a torsion-free module

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#abstract-algebra #modules #tensor-products #dedekind-domain
1.4k
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Why is the Ideal Norm Multiplicative?

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335
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Completion of a torsion-free module

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#abstract-algebra #modules #tensor-products #dedekind-domain
542
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Is the completion of a Dedekind domain a PID?

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#abstract-algebra #ring-theory #dedekind-domain
161
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How to prove this innocent looking isomorphism

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