English

Rings Whose Non-Invertible Elements Are Uniquely Strongly Clean

Rings and Algebras 2024-01-09 v1

Abstract

We define and explore in details the class of GUSC rings, that are those rings whose non-invertible elements are uniquely strongly clean. These rings are a common generalization of the so-called USC rings, introduced by Chen-Wang-Zhou in J. Pure & Appl. Algebra (2009), which are rings whose elements are uniquely strongly clean. These rings also generalize the so-called GUC rings, defined by Guo-Jiang in Bull. Transilvania Univ. Bra\c{s}ov (2023), which are rings whose non-invertible elements are uniquely clean.

Keywords

Cite

@article{arxiv.2401.03320,
  title  = {Rings Whose Non-Invertible Elements Are Uniquely Strongly Clean},
  author = {Peter Danchev and Omid Hasanzadeh and Ahmad Moussavi},
  journal= {arXiv preprint arXiv:2401.03320},
  year   = {2024}
}

Comments

12 pages

R2 v1 2026-06-28T14:10:19.696Z