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We show that if a non-associative unital ring is graded by a hypercentralgroup, then the ring is simple if and only if it is graded simple and thecenter of the ring is a field. Thereby, we extend a result by Jespers to anon-associative setting. By applying this result to non-associative crossedproducts, we obtain non-associative analogues of results by Bell, Jordan andVoskoglou. We also apply our result to Cayley-Dickson doublings, therebyobtaining a new proof of a classical result by McCrimmon.

Simple graded rings, non-associative crossed products and Cayley-Dickson doublings