0
votes
1answer
59 views

$Tor_1^\mathbb{Z}(\mathbb{Z}/2\mathbb{Z}, \mathbb{Z}/2\mathbb{Z})$

How do I find $Tor_1^\mathbb{Z}(\mathbb{Z}/2\mathbb{Z}, \mathbb{Z}/2\mathbb{Z})$? and is it free or at least projective? I tried using the obvious short exact sequence then tensoring with ...
2
votes
1answer
133 views

Example computation of $\operatorname{Tor_i}{(M,N)}$

Let $M = \mathbb Z / 284 \mathbb Z$ and $N = \mathbb Z / 2 \mathbb Z$. Can you tell me if my computation of $\operatorname{Tor_i}{(M,N)}$ is correct: (i) First we want a projective resolution of ...
3
votes
1answer
186 views

$\mathrm{Tor}$ functor not left exact

Is there an example which shows that the functor $B\otimes_R(-)$ is not left-exact, given a ring $R$ and a right $R$-module $B$?