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Results tagged with modules
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user 23950
For questions on modules over rings.
4
votes
2
answers
1k
views
When does a faithful module have an element with zero annihilator?
This is a follow up of the question Example of a finitely generated faithful torsion module over a commutative ring on MathSE.
Let $M$ be a finitely generated module over a commutative ring $R$ with …
- 1,313
1
vote
0
answers
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Flatness over a local noetherian ring
Let $(R,\mathfrak m)$ be a local noetherian ring, and $M$ an arbitrary $R$-module. Suppose that $\mathrm{Tor}_1(M,R/\mathfrak m)=0$. Does it follow that $M$ is flat?
The answer is positive when $M$ …
- 1,313