Let R be a commutative ring, A = A0⊕A1⊕ ... a graded R-algebra, and A+ the graded ideal A1⊕A2⊕... Then Ki(A) = Ki(A0)⊕Ki(A, A+). We show that the groups Ki(A, A+) are naturally modules over the ring W(R) of Witt vectors. They also have a natural filtration whose associated graded groups are R-modules. When R contains a field of characteristic zero, Ki(A,A +) is an R-module, and the filtration is by R-Submodules.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory