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We define and explore in details the class of GUSC rings, that are thoserings whose non-invertible elements are uniquely strongly clean. These ringsare a common generalization of the so-called USC rings, introduced byChen-Wang-Zhou in J. Pure & Appl. Algebra (2009), which are rings whoseelements are uniquely strongly clean. These rings also generalize the so-calledGUC rings, defined by Guo-Jiang in Bull. Transilvania Univ. Bra\c{s}ov (2023),which are rings whose non-invertible elements are uniquely clean.

Rings Whose Non-Invertible Elements Are Uniquely Strongly Clean