Q) Put True (T) or Fuls (F) for the following: (1)Every prime ideal I of ring R is maximal ideal. (2) Every non-zero idempotent element in ring R is zero divisor in R. (3)A non-zero idempotent element cannot be nilpotent. (4) For any element a in a Boolean ring R, then 4a=0.

Q) Put True (T) or Fuls (F) for the following: (1)Every prime ideal I of ring R is maximal ideal. (2) Every non-zero idempotent element in ring R is zero divisor in R. (3)A non-zero idempotent element cannot be nilpotent. (4) For any element a in a Boolean ring R, then 4a=0.

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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Question

Q) Put True (T) or Fuls (F) for the following:
(1) Every prime ideal I of ring R is maximal ideal.
(2) Every non-zero idempotent element in ring R is zero divisor in R.
(3) A non-zero idempotent element cannot be nilpotent.
(4) For any element a in a Boolean ring R, then 4a=0.

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