Let R be a ring with unit. Define 2R ≔ 1R + 1R. In most rings, 2R ≠ 1R. Figure out what the condition is, and then prove that under the assumption of that condition, 2R ≠ 1R.
Let R be a ring with unit. Define 2R ≔ 1R + 1R. In most rings, 2R ≠ 1R. Figure out what the condition is, and then prove that under the assumption of that condition, 2R ≠ 1R.
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 37E: 37. Let and be elements in a ring. If is a zero divisor, prove that either or is a zero...
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Let R be a ring with unit. Define 2R ≔ 1R + 1R. In most rings, 2R ≠ 1R. Figure out what the condition is, and then prove that under the assumption of that condition, 2R ≠ 1R.
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