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We define the class of {\it CUSC} rings, that are those rings whose cleanelements are uniquely strongly clean. These rings are a common generalizationof the so-called {\it USC} rings, introduced by Chen-Wang-Zhou in J. Pure \&Applied Algebra (2009), which are rings whose elements are uniquely stronglyclean. These rings also generalize the so-called {\it CUC} rings, defined byCalugareanu-Zhou in Mediterranean J. Math. (2023), which are rings whose cleanelements are uniquely clean. We establish that a ring is USC if, and only if,it is simultaneously CUSC and potent. Some other interesting relationships withCUC rings are obtained as well.

Rings Whose Clean Elements Are Uniquely Strongly Clean