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Faithfully flat change of ring in the tensor product

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#commutative-algebra #tensor-products #flatness
102
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Example of a universally injective ring morphism which is not faithfully flat

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#commutative-algebra #flatness
126
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Flat locus of finite map between integral schemes is not necessarily open

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#algebraic-geometry #flatness #blowup
33
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References for examples of flat and non flat morphisms with solutions?

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#algebraic-geometry #flatness
155
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Étale covering of nodal cubic curve, Hartshorne exercise 10.6.

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#algebraic-geometry #curves #algebraic-curves #flatness
92
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Is the following ideal prime or the following quotient ring flat?

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#commutative-algebra #ideals #maximal-and-prime-ideals #flatness
43
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Example of absolutely flat semi-artinian ring

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#commutative-algebra #flatness #artinian
69
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Flatness of $\mathbb{C}[x_1,\ldots,x_n]$ over $\mathbb{C}[f]$, $f \in \mathbb{C}[x_1,\ldots,x_n]$, $n \geq 1$

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#algebraic-geometry #polynomials #commutative-algebra #free-modules #flatness
48
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Let $f: N \rightarrow P$, $M$ faithfully flat iff $\alpha \otimes id_M = 0$

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#commutative-algebra #flatness
73
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If $M$ is a flat $A$-module, then is $M$ a flat $A/I$ module?

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#abstract-algebra #commutative-algebra #modules #flatness
102
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$\mathbb{Q}$ with trivial $R$-module structure is flat

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#commutative-algebra #modules #flatness
107
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How to determine flatness

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#commutative-algebra #flatness
61
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Is Every Isomorphism on Tensor Product of Modules an R-module Isomorphism?

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#abstract-algebra #modules #localization #projective-module #flatness
41
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How Can We Prove Flatness from an Induced Exact Sequence?

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#abstract-algebra #modules #projective-module #flatness #injective-module
40
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$R$ points of derived subgroup of algebraic group

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#group-theory #algebraic-geometry #algebraic-groups #flatness #derived-subgroup

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