Let $\overline{\mathbb{R}}_{\geq 0} = \mathbb{R}_{\geq 0} \cup \{\infty\}$. Does there exist an example of the following? A commutative ring with unity $R$ A mapping $\operatorname{d}: R\operatorname{-Mod} \to \overline{\mathbb{R}}_{\geq 0}$ with the following properties: If $A \cong B$, $\oper...