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}
}
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12 pages