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Commutative rings and Nilpotent Elements

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Let R be a commutative ring with 1 not equal to zero. Prove that if "a" is a nilpotent element of R then 1-ab is a unit for all "b" in R.

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since a is nilpotent, there is a positive integer n such that a^n = 0

observe that, in particular if ...

Solution Summary

Commutative rings and nilpotent elements are investigated.