Geodesic
Rings whose non-invertible elements are weakly nil-clean
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 35 (2025) no. 1, pp. 47-74

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In regard to our recent studies of rings with (strongly, weakly) nil-clean-like properties, we explore in-depth both the structural and characterization properties of those rings whose elements that are not units are weakly nil-clean. Group rings of this sort are considered and described as well. This somewhat supplies our recent results of this branch when the units are weakly nil-clean published in Punjab University Journal of Mathematics (2024).
Keywords: idempotent, nilpotent, unit, weakly nil-clean ring 
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P. V. Danchev; O. Hasanzadeh; A. Javan; A. Moussavi. Rings whose non-invertible elements are weakly nil-clean. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 35 (2025) no. 1, pp. 47-74. http://geodesic.mathdoc.fr/item/VUU_2025_35_1_a2/