October 3, 2025Open Access

Weakly Strongly 2-Nil-Clean Rings

Key Points

Weakly strongly 2-nil-clean rings are a generalization of both strongly 2-nil-clean and strongly weakly nil-clean rings.
Any weakly strongly 2-nil-clean ring is proven to be strongly π-regular, showcasing its structural stability.
These rings can be decomposed into a direct product of a strongly 2-nil-clean ring and a specific ring type.
The findings contribute significant insights to the field of algebra and ring theory, impacting future research.

Abstract

In this paper, we introduce and explore in-depth the notion of 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 π-regular and, concretely, it decomposes as the direct product of a strongly 2-nil-clean ring and a ring of the type Z₂㵮 for some k 1.

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Cite This Study

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

synapsesocial.com/papers/68e034f7f0e39f13e7fa3072 https://doi.org/https://doi.org/10.48550/arxiv.2509.05673

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