Timeline for What conditions are needed for $-\otimes_A B$ to be faithful?
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2010 at 18:44 | comment | added | Greg Muller | I had missed the requirement that $B$ was a ring, rather than an $A$-module. Of course, I can replace $B$ by its symmetric tensor algebra to get a ring which is faithful but not flat. | |
| Dec 2, 2010 at 18:09 | vote | accept | Ketil Tveiten | ||
| Dec 2, 2010 at 17:57 | comment | added | Karl Schwede | @Greg, do you know of any examples of commutative rings $B$ with unity? | |
| Dec 2, 2010 at 17:41 | comment | added | Achilleas K | Yes. I have now replaced "faithfully flat" to "faithful" in my answer. | |
| Dec 2, 2010 at 17:37 | history | edited | Achilleas K | CC BY-SA 2.5 |
deleted 7 characters in body; added 2 characters in body
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| Dec 2, 2010 at 17:29 | comment | added | Greg Muller | Yes, it is possible to be faithful without being flat. Let $A=k[x,y]$ and let $B= xA+yA$. | |
| Dec 2, 2010 at 15:55 | comment | added | Graham Leuschke | Why must $B$ be flat? Seems like this is the content of the earlier question -- is it possible for $-\otimes_AB$ to be faithful without $B$ being flat. | |
| Dec 2, 2010 at 15:52 | vote | accept | Ketil Tveiten | ||
| Dec 2, 2010 at 18:09 | |||||
| Dec 2, 2010 at 14:41 | history | answered | Achilleas K | CC BY-SA 2.5 |