Let R be a finite ring with identity. Which of the following statements is true? O None of the choices O Every non-zero element of R is either a unit or a zero divisor. O Every non-zero element of R is a zero divisor. O Every non-zero element of R is a unit.
Let R be a finite ring with identity. Which of the following statements is true? O None of the choices O Every non-zero element of R is either a unit or a zero divisor. O Every non-zero element of R is a zero divisor. O Every non-zero element of R is a unit.
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 5TFE: True or False Label each of the following statements as either true or false. If one element in a...
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![Let R be a finite ring with identity. Which of the following statements is
true?
O None of the choices
O Every non-zero element of R is either a unit or a zero divisor.
O Every non-zero element of R is a zero divisor.
O Every non-zero element of R is a unit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F650bea2c-2cbd-4572-bb26-a17625a0ead9%2F0bbf0e55-e651-497c-b9a6-1df150189b36%2Fuev5sxg_processed.png&w=3840&q=75)
Transcribed Image Text:Let R be a finite ring with identity. Which of the following statements is
true?
O None of the choices
O Every non-zero element of R is either a unit or a zero divisor.
O Every non-zero element of R is a zero divisor.
O Every non-zero element of R is a unit.
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