has a rank

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

Title	has a rank
Canonical name	HasARank
Date of creation	2013-03-22 18:13:41
Last modified on	2013-03-22 18:13:41
Owner	yshen (21076)
Last modified by	yshen (21076)
Numerical id	6
Author	yshen (21076)
Entry type	Definition
Classification	msc 13C99