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Results tagged with modules
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user 450
For questions on modules over rings.
21
votes
Accepted
Flat module and torsion-free module
Dear liu,
1) If $A$ is a domain in which every finitely generated ideal is principal, then a module over $A$ is flat iff it is torsion free (Bourbaki, Comm.Alg.,I,§2, 4, Prop.3). Of course a PID has …
- 47.5k
27
votes
Wikipedia's definition of 'locally free sheaf'
Dear roger123, let $R$ be a commutative ring and $M$ an $R$-module ( which I do not suppose finitely generated). In order to minimize the risk of misunderstandings, allow me to introduce the followin …
- 47.5k
13
votes
Justification of the term "invertible sheaf"
It is enough to prove the
REDUCTION Let $M,N$ be $A$- modules such that $M \otimes_A N\cong A$. Then $M$ is projective of finite type. …
- 47.5k
43
votes
Accepted
Rank of a module
Bibliography
Ischebeck and Rao have published a monograph Ideals and reality: projective modules and number of generators of ideals on exactly this theme …
- 47.5k