THE GROTHENDIECK GROUPS OF POLYNOMIAL RINGS AND GROUP RINGS

In this paper,we gave the Grothendieck groups of sonte polynomial rings and group rings. We obtained if R is a noetherian semi-local ring with gl. dim R<∝,G is a finitely generated abelian group,then K0RG≌Z^n for some n>0,where one of the following conditions is satisfied: (1). |TorG| is invertible in R.(2). charR=p^s for some s≥1.

In this paper,we gave the Grothendieck groups of some polynomial rings and group rings. We obtained if R is a noetherian semi - local ring with gl. dim R<∝ ,G is a finitely generated abelian group,then K0RG≌Zn for some n>0 ,where one of the following conditions is satisfied; (1). |TorG| is invertible in R. (2). charR = p for some s≥1.