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Let-R-be-a-cummutative-ring-with-1-and-a-b-R-suppose-a-is-ivertible-and-b-is-nilpotent-Show-that-a-b-is-ivertible-




Question Number 12794 by tawa last updated on 01/May/17
Let R be a cummutative ring with 1, and  a,b∈R. suppose a is ivertible and  b is nilpotent. Show that  a + b  is ivertible.
$$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{cummutative}\:\mathrm{ring}\:\mathrm{with}\:\mathrm{1},\:\mathrm{and}\:\:\mathrm{a},\mathrm{b}\in\mathrm{R}.\:\mathrm{suppose}\:\mathrm{a}\:\mathrm{is}\:\mathrm{ivertible}\:\mathrm{and} \\ $$$$\mathrm{b}\:\mathrm{is}\:\mathrm{nilpotent}.\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{a}\:+\:\mathrm{b}\:\:\mathrm{is}\:\mathrm{ivertible}. \\ $$

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