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Let R be a ring. Suppose that there exist an element r ∈ R with r^n =0, for some n ≥ 1. Prove that 1-r is invertible.

Git Gud
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Amitesh Pal
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1 Answers1

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Hint: $ (1-r)(1+r+r^2+\cdots+r^{m-1})=1-r^m. $ (Why?)

user134824
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