# has a rank

Let $R$ be a Noetherian ring with total quotient ring $\operatorname{Quot}(R)$, and $M$ a finitely generated $R$-module. We say $M$ has a rank if $M\otimes_{R}\operatorname{Quot}(R)\cong\operatorname{Quot}(R)^{n}$ for some non-negative integer $n$. And in this situation, we say $M$ has rank $n$.

Title has a rank HasARank 2013-03-22 18:13:41 2013-03-22 18:13:41 yshen (21076) yshen (21076) 6 yshen (21076) Definition msc 13C99