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Sorted by: 6. It is a theorem of Jacobson that any ring whose elements satisfy xn = x x n = x for a particular n n is commutative. For n = 3 n = 3, if we restrict ourselves to examples of characteristic 3 3 then I suspect all examples are given by the ring of continuous functions T → F3 T → F 3 for a Stone space T T (I think you can more or.
