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We introduce the class of epsilon-strongly graded rings and show that itproperly contains both the class of strongly graded rings and the class ofunital partial crossed products. We determine precisely when anepsilon-strongly graded ring is separable over its principal component.Thereby, we simultaneously generalize a result for strongly group graded ringsby Nastasescu, Van den Bergh and Van Oystaeyen, and a result for unital partialcrossed products by Bagio, Lazzarin and Paques. We also show that the class ofunital partial crossed products appear in the class of epsilon-strongly gradedrings in a fashion similar to how the classical crossed products presentthemselves in the class of strongly graded rings. Thereby, we obtain, in thespecial case of unital partial crossed products, a short proof of a generalresult by Dokuchaev, Exel and Sim\'{o}n concerning when graded rings can bepresented as partial crossed products. We also provide some interesting classesof examples of separable epsilon-strongly graded rings, with finite as well asinfinite grading groups. In particular, we obtain an answer to a questionraised by Le Bruyn, Van den Bergh and Van Oystaeyen in 1988.

Epsilon-strongly graded rings, separability and semisimplicity