Answer to Question #18079 in Abstract Algebra for john.george.milnor

Question #18079

Let J be an ideal in any ring R. Suppose J^n+1 = 0 (so in particular, J ⊆ rad(R)). Show that 1 + J is a nilpotent group of class ≤ n; that is, 1 + J has a central series of length ≤ n.

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