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arXiv · 2509.05673

Weakly Strongly 2-Nil-Clean Rings

Peter Danchev·Mina Doostalizadeh·Ahmad Moussavi
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Abstract

In this paper, we introduce and explore in-depth the notion of {\it weakly strongly 2-nil-clean rings} as a common non-trivial generalization of both strongly 2-nil-clean rings and strongly weakly nil-clean rings as defined and studied by Chen-Sheibani in the J. Algebra \& Appl. (2017). We, specifically, succeeded to prove that any weakly strongly 2-nil-clean ring is strongly $\pi$-regular and, concretely, it decomposes as the direct product of a strongly 2-nil-clean ring and a ring of the type $\mathbb{Z}_{2^k}$ for some $k\geq 1$.

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Peter Danchev, Mina Doostalizadeh, Ahmad Moussavi. 2025-09-06. Weakly Strongly 2-Nil-Clean Rings. https://arxiv.org/abs/2509.05673

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