Let R be a commutative ring, a, b e R and ab is a zero-divisor. Show that either a or b is a zero-divisor. We start the proof by (ab) e = 0, c+0. Which of the following is a true statement in the proof? If ac = 0 then a = 0 0 If ac + 0 then b = 0 If ac = 0 then a is a zero divisor If bc = 0 then a = 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 20E
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Let R be a commutative ring, a, b e R and ab is a zero-divisor. Show that either a or b is a zero-divisor.
We start the proof by
(ab) e = 0, e# 0.
Which of the following is a true statement in the proof?
If ac = 0 then a = 0
If ac + 0 then b = 0
If ac = 0 then a is a zero divisor
If bc = 0 then a = 0
Transcribed Image Text:Let R be a commutative ring, a, b e R and ab is a zero-divisor. Show that either a or b is a zero-divisor. We start the proof by (ab) e = 0, e# 0. Which of the following is a true statement in the proof? If ac = 0 then a = 0 If ac + 0 then b = 0 If ac = 0 then a is a zero divisor If bc = 0 then a = 0
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