Inductive Theorems and the Structure of Projective Modules over Crossed Group Rings

摘要

It is proved that the Grothendieck functor and the Swan-Gersten higher algebraic K-functors of a crossed group ring R[π,σρ] are Frobenius modules. As the corollaries an induction theorem for this functors and a reduction theorem for finitely generated R[π,σρ]-projective modules (if R is a discrete normalization ring) are proved. Under some restrictions on n = (π : 1) it is shown that finitely generated R[π,σρ]-projective modules are decomposed into the direct sum of left ideals of the ring R[π,σρ]. More stronger results are proved, when σ = id.