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Results tagged with tensor-products
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user 66686
6
votes
1
answer
499
views
If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
Let $\mathbb{C}$ be the field of the complex numbers. Let $R=\mathbb{C}[x]$, $T=\mathbb{C}\langle x\rangle$ be the ring of entire series with convergence radius at least $1$, and let $S=\mathbb{C}\lan …
- 1,479
2
votes
Accepted
If $M\otimes_S T$ is an $A$-module, is $M$ an $A$-module?
I may have a counter-example. Suppose $A$ is $\mathbb{C}[x,t]/(t^2=x+1)$, and let $M$ be $\mathbb{C}\langle \langle x\rangle\rangle $ as an $S$-module. Then, $M\otimes_S T=\mathbb{C}\langle x\rangle $ …
- 1,479
3
votes
0
answers
158
views
Multiplicative structure on Čech–Alexander complexes
I have the following basic question on Čech–Alexander complexes.
Let $R$ be a ring and $A$ be an $R$-algebra. To this datum one can attach a cosimplicial ring which assigns to an object $[n]=\{0,1,\do …
- 1,479