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arXiv · 2401.03320

Rings Whose Non-Invertible Elements Are Uniquely Strongly Clean

Peter Danchev·Mehrdad Esfandiar·Omid Hasanzadeh
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Abstract

We define and investigate in details the class of so-termed {\it GUSC} rings, that are those rings whose non-invertible elements are uniquely strongly clean. These rings are a common non-trivial generalization of the so-called {\it 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 properly generalize the so-named {\it 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.

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Peter Danchev, Mehrdad Esfandiar, Omid Hasanzadeh. 2024-01-06. Rings Whose Non-Invertible Elements Are Uniquely Strongly Clean. https://arxiv.org/abs/2401.03320

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