Timeline for Direct product of direct sum of a flat module
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 26 at 6:41 | vote | accept | karparvar | ||
| Aug 26 at 5:53 | history | edited | Denis T | CC BY-SA 4.0 |
added 3 characters in body
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| Aug 25 at 18:00 | history | edited | Denis T | CC BY-SA 4.0 |
rewritten the answer to give a (more) complete argument, improved references
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| Aug 23 at 21:03 | comment | added | Denis T | Product of pure monomorphisms is again pure. This can be deduced directly, or by noticing that monomorphism $f: M \to N$ is pure iff $f^+: N^+ \to M^+$ is a split epi, where $M^+$ is $Hom_{\Bbb Z}(M, \Bbb Q / \Bbb Z)$. | |
| Aug 23 at 19:52 | comment | added | karparvar | If I well understand your reasoning, the direct sum $V^{(B)}$ is a pure submodule of $V^A$. Now, if $(V^{(B)})^A$ is a pure submodule of $(V^B)^A$, then by your argument and the hypothesis of the problem, we are done. But, how do we get the pureness of the direct product $(V^{(B)})^A$ in the direct product $(V^B)^A$? If I am not right, would you please explain more. | |
| Aug 23 at 14:50 | history | answered | Denis T | CC BY-SA 4.0 |