G-theory

Summary

G-theory is the K-theory of all finitely generated modules over a Noetherian ring, rather than only the projective ones. Its first group $G_0(R)$ is the Grothendieck group of the abelian category of finitely generated $R$-modules, and the higher groups $G_n(R)$ come from Quillen's construction. It is also called the K-theory of coherent sheaves, or K'-theory, and it has good localization properties. For a regular Noetherian ring it agrees with algebraic K-theory, by the resolution theorem.