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Rings Whose Non-Invertible Elements Are Nil-Clean (2405.09961v1)
Published 16 May 2024 in math.RA and math.RT
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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