Year: 2024
Type: preprint
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. Braşov (2023), which are rings whose non-invertible elements are uniquely clean.
Source: arXiv (Cornell University)
Authors: Danchev, Peter, Esfandiar, Mehrdad, Hasanzadeh, Omid
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4390722937