Rings Whose Non-Invertible Elements Are Uniquely Strongly Clean

We define and explore in details the class of GUSC rings, that are those rings whose non-invertible elements are uniquely strongly clean. These rings are a common generalization of the so-called USC rings, introduced by Chen-Wang-Zhou in J. Pure & Appl. Algebra (2009), which are rings whose elements are uniquely strongly clean. These rings also generalize the so-called GUC rings, defined by Guo-Jiang in Bull. Transilvania Univ. Braşov (2023), which are rings whose non-invertible elements are uniquely clean.