Timeline for Double dual of free $\mathbb{Z}_{(p)}$-modules
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2023 at 9:09 | comment | added | Neil Strickland | I think that if $R$ is any proper subring of $\mathbb{Q}$ then we can choose a prime $p$ that is not invertible in $R$ and use the above argument to show that $\chi\colon F\to\text{Hom}(\text{Hom}(F,R),R)$ is an isomorphism whenever $F$ is free and countable. Essentially the same argument shows that $\chi$ is a split monomorphism whenever $F$ is free, even if it is uncountable. If I understand correctly, there is some story relating the cokernel to ultrafilters and measurable cardinals. | |
| Aug 31, 2023 at 8:24 | history | edited | Jeremy Rickard | CC BY-SA 4.0 |
added 1 character in body
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| Aug 31, 2023 at 7:52 | vote | accept | Neil Strickland | ||
| Aug 31, 2023 at 7:28 | history | answered | Jeremy Rickard | CC BY-SA 4.0 |