37. An element x in a ring is called an idempotent if x2 = x. Prove that the only idempotents in an integral domain are 0 and 1. Find a ring with a idempotent a not equal to 0 or 1.

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 38E: An element x in a ring is called idempotent if x2=x. Find two different idempotent elements in M2().
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Abstract Algebra:

37. An element x in a ring is called an idempotent if x2
= x. Prove that the only
idempotents in an integral domain are 0 and 1. Find a ring with a idempotent a
not equal to 0 or 1.
Transcribed Image Text:37. An element x in a ring is called an idempotent if x2 = x. Prove that the only idempotents in an integral domain are 0 and 1. Find a ring with a idempotent a not equal to 0 or 1.
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