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Fraction field of $R/P$

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#abstract-algebra #ring-theory #commutative-algebra
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What is the intuition behind the name "Flat modules"?

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#commutative-algebra #definition #intuition
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Spectrum of a product of rings isomorphic to the product of the spectra

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#abstract-algebra #ring-theory #commutative-algebra #ideals
192
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Example of Localization and Prime Ideals

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#ring-theory #commutative-algebra #examples-counterexamples #ideals
179
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Is the homomorphic image of a G-domain is G-domain?

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#ring-theory #commutative-algebra
216
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kernel of k-homomorphism

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#abstract-algebra #commutative-algebra
401
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Exercise from Atiyah about flatness

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#abstract-algebra #ring-theory #commutative-algebra #homological-algebra
189
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Approximating modules over complete local rings

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#commutative-algebra #modules #noetherian
84
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Equality with powers of an ideal

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#abstract-algebra #ring-theory #commutative-algebra #ideals #noetherian
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Exercise 2.11 Atiyah-Macdonald

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#abstract-algebra #ring-theory #commutative-algebra
80
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$\operatorname{Hom}_\Lambda (B, \operatorname{Hom}_{\Bbb Z}(\Lambda, X)) = \operatorname{Hom}_\Bbb Z (B, X)$

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#commutative-algebra
467
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Exercise 2.26 Atiyah-Macdonald, flatness

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#abstract-algebra #ring-theory #commutative-algebra #modules #homological-algebra
603
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Localization in formal power series

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#abstract-algebra #commutative-algebra #algebraic-number-theory
298
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Converse of fundamental theorem of finitely-generated modules

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#commutative-algebra
838
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In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?

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#commutative-algebra

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