Exercise 8.2. An element a of a ring R is nilpotent if an = 0 for some n Є N.(1) Show that if R is commutative and a, b are nilpotent elements of R, then a + b is alsonilpotent.(2) How about when R is NOT commutative?

Step 1: (1): When R is CommutativeWe need to show that if R is a commutative ring and a and b are…

Answered: Exercise 8.2. An element a of a ring R…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.1: Definition Of A Ring

Problem 49E: An element a of a ring R is called nilpotent if an=0 for some positive integer n. Prove that the set...

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Exercise 8.2. An element a of a ring R is nilpotent if an = 0 for some n Є N. (1) Show that if R is commutative and a, b are nilpotent elements of R, then a + b is also nilpotent. (2) How about when R is NOT commutative?