Strongly clean ring elements that are one-sided inverses
Abstract
A longstanding open question is whether every strongly clean ring is Dedekind-finite (definitions recalled below). We give an example of a ring with a pair of strongly clean elements that are one-sided, but not two-sided inverses of one another, suggesting that the answer to that question may be negative. [Formula: see text] We discuss possible ways of strengthening this result to give a full negative answer. We end with some brief observations on related topics, in particular, uniquely strongly clean rings.
Fields of Study & Subjects
Matrix Theory and Algorithms
Advanced Mathematical Modeling in Engineering
Algebraic and Geometric Analysis
Publication details
- Journal / source
- International Journal of Algebra and Computation
- Pages
- 1–8
- Publication date
- 14 May 2026
- Language
- EN