Higher Rank Class Groups by Luther Claborn and Robert Fossum

Let A be a noetherian ring which is locally Macaulay. For each integer i ^ O , groups d(A) and Wi(A) are denned, each sequence of groups generalizing to higher dimensions the usual class group of an integrally closed noetherian domain. d(A) is called the ith class group of A, and Wi(A) is called the ith homologuai class group of A. The main purpose of this note is to show that both sequences of groups have properties analogous to the class group of a Noetherian integrally closed integral domain, and finally to establish a connection between them.