States Functoriality of K_0 Under Extension of Scalars: For each unital ring A, let V(A) denote the commutative monoid of isomorphism classes of finitely generated projective left A-modules under direct sum, let K_0(A) denote the Grothendieck group completion of V(A), and let _A:V(A) K_0(A) denote the canonical monoid homomorphism.