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15
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Why are morphisms in the derived category spans, not cospans?

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#category-theory #homological-algebra #localization
1.2k
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What is the localization of $\mathbb{Z}_{(p)}$ at $p\mathbb{Z}_{(p)}$?

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#localization #maximal-and-prime-ideals #local-rings
146
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On the proof of the going-up and down theorem

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#ring-theory #commutative-algebra #tensor-products #proof-explanation #localization
211
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Show existence of surjective homomorphism from ring of polynomials to ring of fractions with $\varphi(x)=1/t$

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#commutative-algebra #localization #ring-homomorphism
823
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Criterion for a locally factorial domain

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#ring-theory #commutative-algebra #maximal-and-prime-ideals #localization #dimension-theory-algebra
147
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The support of a finitely generated module and its naturality

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#commutative-algebra #modules #maximal-and-prime-ideals #localization
721
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Minimum number of generators of a module and its 'local dimension'

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#ring-theory #commutative-algebra #modules #localization
804
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Localization preserves UFDs using Kaplansky criterion

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#abstract-algebra #localization #unique-factorization-domains
366
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Non-locally factorial domain

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#abstract-algebra #ring-theory #commutative-algebra #examples-counterexamples #localization
267
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Quasicoherent sheaf of finite type

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#algebraic-geometry #commutative-algebra #localization #limits-colimits
1.6k
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Proof check: being reduced is a local property (Atiyah-Macdonald 3.5)

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#abstract-algebra #ring-theory #commutative-algebra #modules #localization
835
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If the localization of a ring at each prime ideal is Noetherian, does this imply that ring is Noetherian?

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#algebraic-geometry #commutative-algebra #noetherian #localization
1.1k
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Localization in graded rings

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#abstract-algebra #localization #graded-rings
183
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Localisation of quotients of Dedekind Domains

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#commutative-algebra #localization
284
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"De-localization" of a Noetherian module?

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#abstract-algebra #algebraic-geometry #commutative-algebra #noetherian #localization

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