Abstract
A ring R is unit nil-clean if, for any $$a\in R$$ , there exists a unit $$u\in R$$ , such that ua is the sum of an idempotent and a nilpotent. In this paper, we completely describe the structure of unit nil-clean rings. We thereby provide a large class of rings over which every square matrix is equivalent to the sum of idempotent and nilpotent matrices. Furthermore, the uniqueness is determined by the abelian property.
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.
