If a and b are nilpotent element of a commutative ring, show that a+b is also nilpotent. Give an example to show that this may fail if the ring is not commutative( maybe using a counterexample (a+b)6=0)

If a and b are nilpotent element of a commutative ring, show that a+b is also nilpotent. Give an example to show that this may fail if the ring is not commutative( maybe using a counterexample (a+b)6=0)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 30E: a. For a fixed element a of a commutative ring R, prove that the set I={ar|rR} is an ideal of R....

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