Tittel: On the tensor product, and defining $Tor^R_n (-, N)$
Veileder: Steffen Oppermann
Sammendrag: The purpose of this thesis is to define $Tor^R_n (-, N)$, and give a geometric invariant defined in terms of $Tor^R_n (M, N)$. The reason to define $Tor^R_n (-, N)$ is the failure of the functor $- \otimes_R N$ to be left exact. With $Tor^R_n (-, N)$ one has found a way of measuring this functors failure of left exactness. The stepping stones to achieve the goal will be to get familiar with the tensor product, and some homological algebra, in form of chain complexes, projectives and left derived functors.