List questions from flatness

Published on 23 Mar 2026 - 0:36

123

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Are $K[X,Y,Z]$, $K[X,Y,Z]/(Z^2)$ and $K[X,Y,Z]/(XZ,YZ,Z^2)$ flat $K[X,Y]$-modules?

Published on 19 Nov 2015 - 22:14

475

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Computing $\text{Tor}$ for modules over a PID

Published on 26 Mar 2026 - 17:38

408

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Understanding tensor products and $R$-algebras

Published on 19 Mar 2026 - 18:10

99

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If $F\cong R^n$, why is $1\otimes \psi\colon F\otimes_R L\to F\otimes_R M$ injective?

Published on 15 Dec 2015 - 2:09

167

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Why Flat module is 'flat'?

Published on 23 Dec 2015 - 7:03

810

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Is $A / \mathfrak{m}$ flat if $A$ is a local ring?

Published on 31 Dec 2015 - 20:03

283

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If $f: A\to B$ is faithfully flat and $B$ is an Artinian ring then $A$ is also Artinian.

Published on 07 Jan 2016 - 13:14

366

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Is the dual of a flat module flat

Published on 26 Mar 2026 - 8:15

228

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Is this ring extension flat?

Published on 08 Feb 2016 - 18:56

168

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Trivialization of flat proper morphisms with sections

Published on 25 Feb 2016 - 4:51

67

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On characterizing modules that don't annihilate any module under tensor product.

Published on 28 Feb 2016 - 14:03

85

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Show that if E is a free right R-module,then $\pi$ is injective

Published on 06 Mar 2016 - 4:46

321

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how to prove the following sequence is exact

Published on 07 Mar 2016 - 1:46

7.1k

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Show that a Z-module A is flat if and only if it is torsion-free?

Published on 07 Mar 2016 - 4:32

List Question

flat morphisms of rings

Are $K[X,Y,Z]$, $K[X,Y,Z]/(Z^2)$ and $K[X,Y,Z]/(XZ,YZ,Z^2)$ flat $K[X,Y]$-modules?

Computing $\text{Tor}$ for modules over a PID

Understanding tensor products and $R$-algebras

If $F\cong R^n$, why is $1\otimes \psi\colon F\otimes_R L\to F\otimes_R M$ injective?

Why Flat module is 'flat'?

Is $A / \mathfrak{m}$ flat if $A$ is a local ring?

If $f: A\to B$ is faithfully flat and $B$ is an Artinian ring then $A$ is also Artinian.

Is the dual of a flat module flat

Is this ring extension flat?

Trivialization of flat proper morphisms with sections

On characterizing modules that don't annihilate any module under tensor product.

Show that if E is a free right R-module,then $\pi$ is injective

how to prove the following sequence is exact

Show that a Z-module A is flat if and only if it is torsion-free?

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