Nil Ideals of Crossed Products

Abstract

Let ℒ(R) and 𝒦(R) be respectively the locally nilpotent radical and the upper nil radical of the ring R. If K _ρ Gis a twisted group ring of a group Gover a ring Kand the order of every torsion element of Gis not a zero divisor in K, then we prove that

Moreover, let K ∗ Gbe a crossed product of a group Gover a prime ring Kof characteristic p ≥ 0. If the subgroup G _inn has no p-elements when p > 0 and 𝒦(K) = O, then 𝒦(K ∗ G) = O.

Key Words:

• Crossed products
• Twisted group rings
• Nil ideals

2000 Mathematics Subject Classification:

• 16S34
• 20C07

Acknowledgment

The research was partly supported by Plovdiv University under contract M 25/2001.