Timeline for Tor functor and invertible elements
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2019 at 7:39 | vote | accept | Boris Bilich | ||
| Nov 3, 2019 at 15:59 | comment | added | SashaP | Got it, just the vanishing of the tensor product already implies that some element of $a$ is invertible if $M$ is finitely generated. | |
| Nov 3, 2019 at 15:58 | answer | added | SashaP | timeline score: 3 | |
| Nov 3, 2019 at 14:23 | comment | added | Boris Bilich | @SashaP, 0th Tor (just tensor product) counts too. In case of $M=A$ we have 0th Tor is isomorphic to $A/a$. | |
| Nov 3, 2019 at 13:51 | comment | added | SashaP | Apparently I’m misunderstanding something, but the vanishing condition holds for any $M$ flat over $A$, in particular for $M=A$ in which case $S$ is the set of invertible elements in $A$ so it has empty intersection with any non-unital ideal. The converse is thus false for every ring $A$. | |
| Nov 2, 2019 at 20:56 | history | edited | Boris Bilich | CC BY-SA 4.0 |
added 166 characters in body
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| Nov 2, 2019 at 20:00 | history | asked | Boris Bilich | CC BY-SA 4.0 |