Nil Clean Involutions
Rings and Algebras
2017-10-03 v2
Abstract
We prove that if an involution in a ring is the sum of an idempotent and a nilpotent then the idempotent in this decomposition must be 1. As a consequence, we completely characterize weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl., DOI: 10.1142/S0219498816501486].
Cite
@article{arxiv.1512.02277,
title = {Nil Clean Involutions},
author = {Janez Šter},
journal= {arXiv preprint arXiv:1512.02277},
year = {2017}
}