Invertible plus nilpotent implies invertible
This article is about the statement of a simple but indispensable lemma in commutative algebra
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Given: A commutative unital ring , elements such that is invertible, and for some positive integer
To prove: is invertible
Proof: Since is invertible, it suffices to prove that is invertible. Since , we also have . The above formula then tells us that is invertible, completing the proof.