English

Rings in which every element is either a sum or a difference of a nilpotent and an idempotent

Rings and Algebras 2014-12-18 v1

Abstract

{Generalizing the notion of nil cleanness from \cite{D13}, in parallel to \cite{DM14}, we define the concept of {\it weak nil cleanness} for an arbitrary ring. Its comprehensive study in different ways is provided as well. A decomposition theorem of a weakly nil-clean ring is obtained. It is completely characterized when an abelian ring is {\it weakly nil-clean}.} It is also completely determined when a matrix ring over a division ring is weakly nil-clean.

Keywords

Cite

@article{arxiv.1412.5544,
  title  = {Rings in which every element is either a sum or a difference of a nilpotent and an idempotent},
  author = {Simion Breaz and Peter Danchev and Yiqiang Zhou},
  journal= {arXiv preprint arXiv:1412.5544},
  year   = {2014}
}

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