K-groups for rings of finite Cohen–Macaulay type

TY - JOUR

T1 - K-groups for rings of finite Cohen–Macaulay type

AU - Holm, Henrik Granau

PY - 2015/7/1

Y1 - 2015/7/1

N2 - For a local Cohen-Macaulay ring R of finite CM-type, Yoshino has applied methods of Auslander and Reiten to compute the Grothendieck group K0 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 K1(mod R). We also describe the group homomorphism R∗ → K1(mod R) induced by the inclusion functor proj R → mod R and illustrate our results with concrete examples.

AB - For a local Cohen-Macaulay ring R of finite CM-type, Yoshino has applied methods of Auslander and Reiten to compute the Grothendieck group K0 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 K1(mod R). We also describe the group homomorphism R∗ → K1(mod R) induced by the inclusion functor proj R → mod R and illustrate our results with concrete examples.

U2 - 10.1515/forum-2013-6029

DO - 10.1515/forum-2013-6029

M3 - Journal article

SN - 0933-7741

VL - 25

SP - 2413

EP - 2452

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 4

ER -