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Journal of Interdisciplinary Mathematics

(Since 1998)
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502
CiteScore 2025: 1.9 (Q2)

CiteScore 2025: 1.9 (Q2)

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Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Journal of Interdisciplinary Mathematics
Open Access Research Article

Rings whose units have identity plus quasi-nilpotent square

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pp. 2027–2047Vol. 29Issue 6June 2026DOI: 10.47974/JIM-2571XML
Received:
01 Sep 2025
Published Online:
30 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2571
Pages:
2027–2047

Abstract

In this paper, we investigate the structural and characterizing properties of the so-called 2-UQ rings, that are rings such that the square of every unit is the sum of an idempotent and a quasi-nilpotent element that commute with each other. We establish some fundamental connections between 2-UQ rings and relevant widely classes of rings including 2-UJ, 2-UU and tripotent rings. Our novel results include: (1) complete characterizations of 2-UQ group rings, showing that they force underlying groups to be either 2-groups or 3-groups when 3∈J(R); (2) Morita context extensions preserving the 2-UQ property when trace ideals are nilpotent; and (3) the discovery that potent 2-UQ rings are precisely the semi-tripotent rings. Furthermore, we determine how the 2-UQ property interacts with the regularity, cleanness and potent conditions. Likewise, certain examples and counter-examples illuminate the boundaries between 2-UQ rings and their special relatives.       These achievements of ours somewhat substantially expand those obtained by Cui and Yin [8] in Commun. Algebra (2020) and by Danchev et al. [12] in J. Algebra & Appl. (2025). 

Keywords

Quasi-nilpotentsUQ rings2-UQ ringsGroup ringsSemi-potent rings

Subject Classifications

16S3416U6020C07

References

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