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Results tagged with flatness
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user 75
20
votes
Accepted
Does projective imply flat?
I believe the following is a counterexample. Let $\mathcal{A}$ and $\mathcal{B}$ be closed symmetric monoidal abelian categories such that the unit object $1\in\mathcal{B}$ is projective and let $F:\ …
- 31.2k
11
votes
Accepted
Injective flat module
Here's a counterexample. Let $k$ be a field and $R=k[x,y]/(x^2,xy,y^2)$; this is a local ring with maximal ideal $m=(x,y)$. Suppose $F$ is a flat $R$-module. Then there is a short exact sequence $$ …
- 31.2k