Answer to Question #18078 in Abstract Algebra for john.george.milnor

Question #18078

Let J be an ideal in any ring R. If J ⊆ rad(R), show that, for any i ≥ 1, the multiplicative group (1 + J^i)/(1 + J^(i+1)) is isomorphic to the additive group J^i/J^i+1.

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