Rings whose non-invertible elements are nil-clean
We systematically study those rings whose nonunits are a sum of an idempotent and a nilpotent. Some crucial characteristic properties are completely described as well as some structural results for this class of rings are obtained. This work somewhat continues two publications on the subject due to A. J. Diesl, Nil clean rings, J. Algebra 383 (2013) 197–211 and A. Karimi–Mansoub, T. Kosan and Y. Zhou, Rings in which every unit is a sum of a nilpotent and an idempotent, Contemp. Math. 715 (2018) 189–203.
Authors
- Peter Danchev (ORCID: https://orcid.org/0000-0002-2016-2336)
- Arash Javan (ORCID: https://orcid.org/0009-0005-4071-6980)
- Omid Hasanzadeh (ORCID: https://orcid.org/0009-0006-1414-4963)
- A. Moussavi (ORCID: https://orcid.org/0000-0002-7775-9782)
Institutions
- Tarbiat Modares University (IR)
- Bulgarian Academy of Sciences (BG)
- Institute of Mathematics and Informatics (BG)
Publication Details
- Journal
- Asian-European Journal of Mathematics
- Published
- 2025-04-25
- DOI
- https://doi.org/10.1142/s1793557125500524
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 0.00