If Ris a commutative ring, then (b) a | b and b|c⇒a | ci.e., this relation of divisibil it y in Ris called transitive relation. (ii) a banda | c⇒a | (b + c) (iii) a | b ⇒ a | bx for all x ≤ R.
If Ris a commutative ring, then (b) a | b and b|c⇒a | ci.e., this relation of divisibil it y in Ris called transitive relation. (ii) a banda | c⇒a | (b + c) (iii) a | b ⇒ a | bx for all x ≤ R.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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![If Ris a commutative ring,
then
(b) a | b and b|c⇒a | ci.e., this relation of divisibil it y
in Ris called transitive relation.
(ii) a | b and a | c⇒a|(b + c)
(iii) a | b ⇒a | bx for all x ≤ R.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd15ec325-f6a8-4c6f-8a02-a0153f1f1664%2F1dbc6550-b5f5-4e58-9955-f244b00b5a3b%2Fncuvurw_processed.png&w=3840&q=75)
Transcribed Image Text:If Ris a commutative ring,
then
(b) a | b and b|c⇒a | ci.e., this relation of divisibil it y
in Ris called transitive relation.
(ii) a | b and a | c⇒a|(b + c)
(iii) a | b ⇒a | bx for all x ≤ R.
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