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If R is a domain and $\lambda$ has non-negative values on objects of $Mod_R$, then $\lambda$ is a multiple of generic rank. See this question Nonnegative additive functions on coherent sheavesNonnegative additive functions on coherent sheaves.
If R is a domain and $\lambda$ has non-negative values on objects of $Mod_R$, then $\lambda$ is a multiple of generic rank. See this question Nonnegative additive functions on coherent sheaves.