May 16, 2024Open Access

Rings Whose Non-Invertible Elements Are Nil-Clean

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Abstract

We systematically study those rings whose non-units are a sum of an idempotent and a nilpotent. Some crucial characteristic properties are completely described as well as some structural results for this class of rings are obtained. This work somewhat continues two publications on the subject due to Diesl (J. Algebra, 2013) and Karimi-Mansoub et al. (Contemp. Math., 2018).

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Danchev et al. (Thu,) studied this question.

synapsesocial.com/papers/68e69d57b6db6435876229af https://doi.org/https://doi.org/10.48550/arxiv.2405.09961

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5On Strongly Nil Gf -Clean Rings and Related Generalized Inverses2026

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