Timeline for term for a "faithful" module
Current License: CC BY-SA 2.5
2 events
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| Nov 30, 2010 at 14:14 | comment | added | Graham Leuschke | In fact, for any local ring $(A, \mathfrak{m})$, $\mathfrak{m} \otimes_A X =0$ implies that $\mathrm{Tor}_1^A(A/\mathfrak{m},X)=\mathfrak{m}X=0$. This says both that $X$ is free and a vector space [which is rare], so as long as $\mathfrak{m} \neq 0$, it is faithful in this sense. | |
| Nov 30, 2010 at 1:45 | history | answered | Greg Marks | CC BY-SA 2.5 |