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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
