Periodic elements and lifting connections

It is well-known that idempotents lift modulo any nil one-sided ideal. While this is not true for periodic elements, it does hold true in many special cases. We investigate the connections between these special cases, as well as limitations. We also answer three questions from the literature. For example, we construct a nilpotent ideal where torsion-units lift, but periodic elements do not lift, modulo that ideal. (c) 2023 Elsevier B.V. All rights reserved.