I'm reading Webb's A Course in Finite Group Representation Theory, but I keep getting stuck on tensor products and keep rereading the definition, but I just don't really understand it.
$R$ is ring and $H\leq G$ subgroup and $V$ an $RH$-module.
$$RH\otimes_{RH}V \cong V$$
So I think the first side of the isomorphism should have elements in the form of $r_1h_1(r_2h_2\otimes v)=rh(1\otimes v)$ for some $r\in R, h\in H$ and $V$ has elements in the form of $rhv$.
So the map
$$rh(1\otimes v) \mapsto rhv $$
should be fine, right?
Thanks in advance!
PS.:Recommendations on books about tensor products (that even I would understand) preferably with exercises and solutions would be welcome!