List questions from flatness

Published on 06 Oct 2017 - 17:39

224

Views

Why is $\text{Hom}_S(k\otimes_R S, M\otimes_R N) \cong \text{Hom}_R(k,M) \otimes_R N$?

Published on 25 Oct 2017 - 1:02

74

Views

Unclear use of the right exactness of $\otimes_R$, isomorphism,projective exact sequence

Published on 27 Oct 2017 - 17:40

242

Views

Ext, obstruction for what is Ext?, Tor is an obstruction for being flat

Published on 27 Oct 2017 - 18:35

71

Views

If $G/H$ is flat $A$-module, and $I$ is an ideal of $A$, $G$ is flat, then how to see $GI\cap H=HI$?

Published on 28 Oct 2017 - 4:07

715

Views

Flatness over a regular local ring of dimension $1$

Published on 06 Nov 2017 - 16:19

366

Views

Example for $R[X]/(rX)$ is a flat $R$-module

Published on 07 Nov 2017 - 10:14

170

Views

About the flatness of a countable infinite direct product

Published on 16 Nov 2017 - 11:03

571

Views

Non-flatness of $k[t]$ as a $k[t^2,t^3]$-module

Published on 23 Feb 2026 - 16:27

224

Views

Showing a module is not flat

Published on 30 Nov 2017 - 5:19

650

Views

A question on finitely generated $k$ algebra

Published on 26 Mar 2026 - 1:02

63

Views

$ \ker(g\otimes I ) =\ker(g) \otimes M, $ where $M$ is faithfully flat.

Published on 05 Dec 2017 - 8:52

315

Views

Ideals and Tensor product by a finitely generated module over Noetherian ring

Published on 06 Dec 2017 - 7:00

729

Views

Flatness implies equi-dimensional fibres

Published on 13 Dec 2017 - 12:55

608

Views

When will open morphisms be flat?

Published on 01 Jan 2018 - 0:25

List Question

Flatness of finitely generated (/finitely presented) module carries to power series module?

Why is $\text{Hom}_S(k\otimes_R S, M\otimes_R N) \cong \text{Hom}_R(k,M) \otimes_R N$?

Unclear use of the right exactness of $\otimes_R$, isomorphism,projective exact sequence

Ext, obstruction for what is Ext?, Tor is an obstruction for being flat

If $G/H$ is flat $A$-module, and $I$ is an ideal of $A$, $G$ is flat, then how to see $GI\cap H=HI$?

Flatness over a regular local ring of dimension $1$

Example for $R[X]/(rX)$ is a flat $R$-module

About the flatness of a countable infinite direct product

Non-flatness of $k[t]$ as a $k[t^2,t^3]$-module

Showing a module is not flat

A question on finitely generated $k$ algebra

$ \ker(g\otimes I ) =\ker(g) \otimes M, $ where $M$ is faithfully flat.

Ideals and Tensor product by a finitely generated module over Noetherian ring

Flatness implies equi-dimensional fibres

When will open morphisms be flat?

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