K-groups for rings of finite Cohen-Macaulay type

摘要

For a local Cohen-Macaulay ring R of finite CM-type, Yoshino has applied methods of Auslander and Reiten to compute the Grothendieck group K-0 of the category mod R of finitely generated R-modules. For the same type of rings, we compute in this paper the first Quillen K-group K-1 (mod R). We also describe the group homomorphism R* --> K-1 (mod R) induced by the inclusion functor proj R --> mod R and illustrate our results with concrete examples.