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arXiv · 2404.10651

Rings whose Non-Invertible Elements are Strongly Nil-Clean

Peter Danchev·Omid Hasanzadeh·Arash Javan·Ahmad Moussavi
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Abstract

We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of commuting nilpotent and idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum of a nilpotent and an unique idempotent. In fact, we succeeded to prove that these two classes of rings can completely be characterized in terms of already well-studied and fully described sorts of rings.

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Peter Danchev, Omid Hasanzadeh, Arash Javan, Ahmad Moussavi. 2024-04-16. Rings whose Non-Invertible Elements are Strongly Nil-Clean. https://arxiv.org/abs/2404.10651

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