Filtrations of modules, the Chow group, and the Grothendieck group (Q1306841)

In this paper the author proves that a finitely generated module over a Noetherian ring defines a unique cycle class in the components with codimension zero and one of the Chow group of the ring. This is an interesting result. It generalizes a classical result over integrally closed domains and implies the isomorphism between the Chow group and the Grothendieck group \((K_0\)-group) under certain conditions. In addition, the author also discusses the difference between the map constructed in this paper and the Riemann-Roch map.