Tensor-nilpotent module
= Tensor-nilpotent module
An $R$-module $M$ is tensor-nilpotent when $M^{\otimes k}=0$ for some positive <integer> $k$. A nonzero <finitely generated module> cannot be tensor-nilpotent: localize at a <maximal ideal> in its support and reduce modulo that <maximal ideal>, obtaining a nonzero tensor power of a nonzero <vector space>.