On Euler characteristic of modules (Q1262376)

Let R be a commutative ring. The author shows that the Euler characteristic is multiplicative on tensor products of stable free R- modules. As an application he obtains the following result: Assuming that there is an isomorphism f: \(K_ 0(R)\to {\mathbb{Z}}\), the Euler characteristic is defined for all finitely generated projective R-modules and coincides with f.