Rings whose Non-Invertible Elements are Strongly Nil-Clean
Rings and Algebras
2024-04-17 v1 Representation Theory
Abstract
We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of commuting nilpotent and idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum of a nilpotent and an unique idempotent. In fact, we succeeded to prove that these two classes of rings can completely be characterized in terms of already well-studied and fully described sorts of rings.
Cite
@article{arxiv.2404.10651,
title = {Rings whose Non-Invertible Elements are Strongly Nil-Clean},
author = {Peter Danchev and Omid Hasanzadeh and Arash Javan and Ahmad Moussavi},
journal= {arXiv preprint arXiv:2404.10651},
year = {2024}
}
Comments
25 pages