On nil clean group rings

Abstract

A ring is nil clean if each of its elements is the sum of an idempotent and a nilpotent. In Sahinkaya et al. [13], it was shown that, for a ring R and a symmetric group S 3, the group ring RS 3 is nil clean iff R and are nil clean. Let be the dihedral group of order 2n and be the generalized quaternion group of order 2n. In this paper, we investigate a more general question and completely characterize when group rings and are nil clean. It is proved that is nil clean iff, either and R is nil clean, or and RS 3 is nil clean, and a similar result is obtained for Furthermore, nil clean group rings with involution * are also investigated.